Areas of Trapezoids, Rhombuses, and Kites. To find the area of a trapezoid, rhombus, or kite
|
|
- Silvia Harper
- 6 years ago
- Views:
Transcription
1 10-2 Areas of Trapezoids, Rombuses, and Kites Common Core State Standards G-MG.A.1 Use geometric sapes, teir measures, and teir properties to describe objects. MP 1, MP 3, MP 4, MP 6 Objective To find te area of a trapezoid, rombus, or kite Rearranging figures into familiar sapes is an example of te Solve a Simpler Problem strategy. Draw a trapezoid on a seet of grap paper. Label te bases b 1 and b 2. Draw its midsegment. Cut out te trapezoid, and ten cut it along te midsegment. Rotate te top part of te trapezoid 180 so tat b 1 and b 2 now form one long base. How can you use tis new figure to find te area of te trapezoid? Explain your reasoning. b 1 b 2 Lesson L VocabularyV eigt of a trapezoid MATHEMATICAL PRACTICES Essential Understanding You can find te area of a trapezoid wen you know its eigt and te lengts of its bases. Te eigt of a trapezoid is te perpendicular distance between te bases. Teorem 10-4 Area of a Trapezoid Te area of a trapezoid is alf te product of te eigt and te sum of te bases. A = 1 2 (b 1 + b 2 ) b 1 b 2 Problem 1 Area of a Trapezoid Wic borders of Nevada can you use as te bases of a trapezoid? Te two parallel sides of Nevada form te bases of a trapezoid. Geograpy Wat is te approximate area of Nevada? A = 1 2 (b 1 + b 2 ) Use te formula for area of a 205 mi trapezoid. = 1 2 (309)( ) Substitute 309 for, 205 for b 1, and 511 for b 2. = 110,622 Simplify. 309 mi Reno Carson City 511 mi Te area of Nevada is about 110,600 mi 2. Las Vegas 1. Wat is te area of a trapezoid wit eigt 7 cm and bases 12 cm and 15 cm? Lesson 10-2 Areas of Trapezoids, Rombuses, and Kites 623
2 Problem 2 Finding Area Using a Rigt Triangle Wat is te area of trapezoid PRS? S 5 m R How are te sides related in a triangle? Te lengt of te ypotenuse is 2 times te lengt of te sorter leg, and te longer leg is 13 times te lengt of te sorter leg. You can draw an altitude tat divides te trapezoid into a rectangle and a triangle. Since te opposite sides of a rectangle are congruent, te longer base of te trapezoid is divided into segments of lengts 2 m and 5 m. = 2 13 longer leg = sorter leg # 13 A = 1 2 (b 1 + b 2 ) Use te trapezoid area formula. = 1 2 (213 )(7 + 5) Substitute 213 for, 7 for b 1, and 5 for b 2. = 1213 Simplify. P P 60 7 m S 5 m 60 2 m 5 m R Te area of trapezoid PRS is Reasoning In Problem 2, suppose decreases so tat m P = 45 wile angles R and and te bases stay te same. Wat is te area of trapezoid PRS? Essential Understanding You can find te area of a rombus or a kite wen you know te lengts of its diagonals. Teorem 10-5 Area of a Rombus or a Kite Te area of a rombus or a kite is alf te product of te lengts of its diagonals. d 1 d 2 d 1 A = 1 2 d 1 d 2 d 2 Rombus Rombus Kite Kite Problem 3 Finding te Area of a Kite Do you need to know te side lengts of te kite to find its area? No. You only need te lengts of te diagonals. Wat is te area of kite KLMN? Find te lengts of te two diagonals: KM = = 7 m and LN = =. Use te formula for area of a kite. A = 1 2 d 1 d 2 = 1 2 (7)(6) Substitute 7 for d 1 and 6 for d 2. = 21 Simplify. K 2 m N L 5 m M Te area of kite KLMN is 21 m Wat is te area of a kite wit diagonals tat are 12 in. and 9 in. long? 624 Capter 10 Area
3 Problem 4 Finding te Area of a Rombus How can you find te lengt of AB? AB is a leg of rigt ABC. You can use te Pytagorean Teorem, a 2 + b 2 = c 2, to find its lengt. Car Pooling Te Hig Occupancy Veicle (HOV) lane is marked by a series of diamonds, or rombuses painted on te pavement. Wat is te area of te HOV lane diamond sown at te rigt? ABC is a rigt triangle. Using te Pytagorean Teorem, AB = = 6. Since te diagonals of a rombus bisect eac oter, te diagonals of te HOV lane diamond are 5 ft and 12 ft. A = 1 2 d 1 d 2 Use te formula for area of a rombus. = 1 2 (5)(12) Substitute 5 for d 1 and 12 for d 2. = 30 Simplify. Te area of te HOV lane diamond is 30 ft 2. A 6.5 ft C B 2.5 ft 4. A rombus as sides 10 cm long. If te longer diagonal is 16 cm, wat is te area of te rombus? Lesson Ceck Do you know HOW? Find te area of eac figure m ft 4. 5 ft m 15 in. 18 in. 27 in. 12 in. 12 in. 2 cm 2 cm 1 cm Do you UNDERSTAND? 7. Vocabulary Can a trapezoid and a parallelogram wit te same base and eigt ave te same area? Explain. b 8. Reasoning Do you need to know all te side lengts to find te area of a trapezoid? 9. Reasoning Can you find te area of a rombus if you only know te lengts of its sides? Explain. 10. Reasoning Do you need to know te lengts of te sides to find te area of a kite? Explain. b MATHEMATICAL PRACTICES Lesson 10-2 Areas of Trapezoids, Rombuses, and Kites 625
4 Practice and Problem-Solving Exercises MATHEMATICAL PRACTICES A Practice Find te area of eac trapezoid See Problem in in. 8.5 cm 9 ft 18 ft 6 ft 9.7 cm 38 in. 14. Find te area of a trapezoid wit bases 12 cm and 18 cm and eigt 10 cm. 15. Find te area of a trapezoid wit bases 2 ft and 3 ft and eigt 1 3 ft. 16. Geograpy Te border of Tennessee resembles a trapezoid wit bases 340 mi and 440 mi and eigt 1i. Estimate te area of Tennessee by finding te area of te trapezoid. Find te area of eac trapezoid. If your answer is not an integer, leave it in simplest radical form. See Problem ft ft 8 ft 6 ft ft 8 m Find te area of eac kite in m 8 in. 8 in. 4 m 8 in. 6 ft 4 ft 4 ft See Problem 3. Find te area of eac rombus in in. 30 ft 20 ft See Problem 4. 5 m B Apply 26. Tink About a Plan A trapezoid as two rigt angles, 12-m and 18-m bases, and an 8-m eigt. Sketc te trapezoid and find its perimeter and area. Are te rigt angles consecutive or opposite angles? How does knowing te eigt elp you find te perimeter? 626 Capter 10 Area
5 27. Metallurgy Te end of a gold bar as te sape of a trapezoid wit te measurements sown. Find te area of te end. 28. Open-Ended Draw a kite. Measure te lengts of its diagonals. Find its area. Find te area of eac trapezoid to te nearest tent ft cm 1 cm 30 9 ft 6.9 cm 4.4 cm 9.2 cm 1.7 m m 0.9 m Coordinate Geometry Find te area of quadrilateral RST. 32. y R 33. y R S x 2 T 2 S 4 x T y S R 2 2 O 2 T 2 x 35. Wat is te area of te kite at te rigt? 90 m m m a. Coordinate Geometry Grap te lines x = 0, x = 6, y = 0, and y = x + 4. b. Wat type of quadrilateral do te lines form? c. Find te area of te quadrilateral. Find te area of eac rombus. Leave your answer in simplest radical form. 9V2 m in m 40. Visualization Te kite as diagonals d 1 and d 2 congruent to te sides of te rectangle. Explain wy te area of te kite is 1 2 d 1 d Draw a trapezoid. Label its bases b 1 and b 2 and its eigt. Ten draw a diagonal of te trapezoid. a. Write equations for te area of eac of te two triangles formed. b. Writing Explain ow you can justify te trapezoid area formula using te areas of te two triangles. d 1 d 2 Lesson 10-2 Areas of Trapezoids, Rombuses, and Kites 627
6 C Callenge 42. Algebra One base of a trapezoid is twice te oter. Te eigt is te average of te two bases. Te area is 324 cm 2. Find te eigt and te bases. (Hint: Let te smaller base be x.) y 43. Sports Ty wants to paint one side of 1 te skateboarding ramp e built. Te y 0.25x ramp is 4 m wide. Its surface is modeled by te equation y = 0.25x 2. Use te trapezoids and triangles O 2 1 sown to estimate te area to be 1 2 painted. 44. In trapezoid ABCD at te rigt, AB } DC. Find te area of ABCD. A 15 in. B x 20 in. 135 D 30 C Standardized Test Prep SAT/ACT Sort Response 45. Te area of a kite is 120 cm 2. Te lengt of one diagonal is 20 cm. Wat is te lengt of te oter diagonal? 12 cm 20 cm 24 cm 48 cm 46. ABC XYZ. AB = 6, BC = 3, and CA = 7. Wic of te following are NOT possible dimensions of XYZ? XY = 3, YZ = 1.5, ZX = 3.5 XY = 10, YZ = 7, ZX = 11 XY = 9, YZ = 4.5, ZX = 10.5 XY = 18, YZ = 9, ZX = Draw an angle. Construct a congruent angle and its bisector. Mixed Review 48. Find te area of a rigt isosceles triangle tat as one leg of lengt 12 cm. 49. A rigt isosceles triangle as area ft 2. Find te lengt of eac leg. 50. Find te measure of an interior angle of a regular nonagon. See Lesson See Lesson 6-1. Get Ready! To prepare for Lesson 10-3, do Exercises Find te area of eac regular polygon. Leave radicals in simplest form cm 10 ft See Lesson Capter 10 Area
Areas of Parallelograms and Triangles 7-1
Areas of Parallelograms and Triangles 7-1 Parallelogram A parallelogram is a quadrilateral where the opposite sides are congruent and parallel. A rectangle is a type of parallelogram, but we often see
More information5.8. Solving Three-Dimensional Problems by Using Trigonometry. LEARN ABOUT the Math. Matt s Solution. 328 Chapter 5
YOU WILL NEE dynamic geometry software (optional) Solving Tree-imensional Problems by Using Trigonometry GOL Solve tree-dimensional problems by using trigonometry. LERN OUT te Mat From point, Manny uses
More informationProperties of Kites and Trapezoids. base of your head to the middle of your back and out to your shoulders.
Kites and Trapezoids Properties of Kites and Trapezoids.3 Learning Goals In this lesson, you will: Construct a kite and a trapezoid. Determine the properties of a kite and a trapezoid. Prove the properties
More information77.1 Apply the Pythagorean Theorem
Right Triangles and Trigonometry 77.1 Apply the Pythagorean Theorem 7.2 Use the Converse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 Apply the Tangent Ratio
More information5-8 Applying Special Right Triangles
5-8 Applying Special Right Triangles Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form. 1. 2. Simplify each
More informationPerimeter and area Test Find the area. A 182 cm 2 B 195 cm 2 C 210 cm 2 D 58 cm 2. 2 Find the area. A 28 yd 2 B 14 yd 2 C 27 yd 2 D 35 yd 2
Name: ate: 1 Find the area. 182 cm 2 195 cm 2 210 cm 2 58 cm 2 2 Find the area. 28 yd 2 14 yd 2 27 yd 2 35 yd 2 opyright Pearson Education, Inc. or its affiliates. ll Rights Reserved. Page 1 of 18 3 Find
More informationChapter 10. Right Triangles
Chapter 10 Right Triangles If we looked at enough right triangles and experimented a little, we might eventually begin to notice some relationships developing. For instance, if I were to construct squares
More informationCK-12 Geometry: Special Right Triangles
CK-12 Geometry: Special Right Triangles Learning Objectives Identify and use the ratios involved with isosceles right triangles. Identify and use the ratios involved with 30-60-90 triangles. Review Queue
More informationLLT Education Services
12. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. 13. There is a slide in a park. One of its side walls has been painted in some colour with a
More informationMath 3 Plane Geometry Review Special Triangles
Name: 1 Date: Math 3 Plane Geometry Review Special Triangles Special right triangles. When using the Pythagorean theorem, we often get answers with square roots or long decimals. There are a few special
More information8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
8-1 The Pythagorean Theorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number 9 Square Positive Square Root 1 4 1 16 Vocabulary Builder leg (noun)
More informationSight Distance. The availability of sufficient sight distance for the driver to see ahead is critical to the design of a safe highway.
Sigt Distance Te availability of sufficient sigt distance for te driver to see aead is critical to te design of a safe igway. Wat is sigt distance? Sigt distance is te lengt of igway visible to a driver.
More informationNAME DATE PERIOD. Areas of Parallelograms and Triangles
11-1 Skills Practice Areas of Parallelograms and Triangles Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 18 mm 10 mm 12 mm 4 ft 60 5.5 ft 4. 14
More informationName: Class: Date: Geometry Chapter 4 Test Review
Name: Class: Date: ID: C Geometry Chapter 4 Test Review. 1. Determine the measure of angle UPM in the following figure. Explain your reasoning and show all your work. 3. Determine the side length of each
More informationMathematics Spiral Review Quarter 2.1 Grade 5
Mathematics Spiral Review Quarter 2.1 Basic Computation (5.NBT.7) Find the sum: 47.8 + 6.23 = Place Value (4.MBT.2) Compare the values using : a) 12 thousands 6 ten thousands b) 24 hundreds 3
More informationDate: Period: Directions: Answer the following questions completely on a separate sheet of paper.
Name: Right Triangle Review Sheet Date: Period: Geometry Honors Directions: Answer the following questions completely on a separate sheet of paper. Part One: Simplify the following radicals. 1) 2) 3) 4)
More informationName Date PD. Pythagorean Theorem
Name Date PD Pythagorean Theorem Vocabulary: Hypotenuse the side across from the right angle, it will be the longest side Legs are the sides adjacent to the right angle His theorem states: a b c In any
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name Date Get Radical or (Be) 2! Radicals and the Pythagorean Theorem Vocabulary Write the term that best completes each statement. 1. An expression that includes
More information8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
8-1 he Pythagorean heorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number Square Positive Square Root 9 81 3 1 4 1 16 1 2 Vocabulary Builder leg
More informationQuadratic Modeling Exercises
Quadratic Modeling Exercises Pages 330 333 Problems 1,5-12,14,15,17,19,21 (for 19 and 21, you re only deciding between linear and quadratic; we ll get to exponential soon!) In class, we analyzed te function
More informationThe Pythagorean Theorem Diamond in the Rough
The Pythagorean Theorem SUGGESTED LEARNING STRATEGIES: Shared Reading, Activating Prior Knowledge, Visualization, Interactive Word Wall Cameron is a catcher trying out for the school baseball team. He
More informationSpecial Right Triangles
GEOMETRY Special Right Triangles OBJECTIVE #: G.SRT.C.8 OBJECTIVE Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling Standard) BIG IDEA (Why is
More informationAbout Finish Line PA Core Math 5
Table of COntents About Finish Line PA Core Math 5 Unit 1: Big Ideas from Grade 4 7 Lesson 1 CC.2.1.4.B.2 Multiplying and Dividing Whole Numbers [connects to CC.2.1.5.B.2] 8 Lesson 2 CC.2.1.4.C.3 Understanding
More informationHow can you compare lengths between the customary and metric systems? 6 ft. ACTIVITY: Customary Measure History
5.7 Converting Measures How can you compare lengts between te customary and metric systems? yd 6 ft ACTIVITY: Customary Measure History COMMON CORE Converting Measures In tis lesson, you will use conversion
More informationCOMPACTED MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED:
COMPACTED MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED: Perimeter of polygons Area of rectangles and squares Area of parallelograms Area of triangles Area of trapezoids Activity 10-1 Perimeter
More information12.3 Using Proportional Relationships
Name lass Date 12.3 Using Proportional Relationsips ssential Question: How can you use similar triangles to solve problems? Resource Locker xplore xploring Inirect Measurement In tis xplore, you will consier
More informationAssignment. Get Radical or (Be) 2! Radicals and the Pythagorean Theorem. Simplify the radical expression. 45x 3 y 7. 28x x 2 x 2 x 2x 2 7x
Assignment Assignment for Lesson.1 Name Date Get Radical or (Be)! Radicals and the Pythagorean Theorem Simplify the radical expression. 1. 60. 60 4 15 15. 8x 5 4. 8x 5 4 7 x x x x 7x 108 108 6 6 45x y
More information3. Find x. 4. FG = 6. m EFG = 7. EH = 8. m FGH = 9. m GFH = 10. m FEH =
1/18 Warm Up Use the following diagram for numbers 1 2. The perpendicular bisectors of ABC meet at D. 1. Find DB. 2. Find AE. 22 B E A 14 D F G C B Use the following diagram for numbers 6. The angle bisectors
More informationPut in simplest radical form. (No decimals)
Put in simplest radical form. (No decimals) 1. 2. 3. 4. 5. 6. 5 7. 4 8. 6 9. 5 10. 9 11. -3 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 3 28. 1 Geometry Chapter 8 - Right Triangles
More informationTEST NAME: G.7 TEST ID: GRADE:08 Eighth Grade SUBJECT: Mathematics TEST CATEGORY:School Assessment
TEST NAME: G.7 TEST ID:877132 GRADE:08 Eighth Grade SUBJECT: Mathematics TEST CATEGORY:School Assessment G.7 Page 1 of 89 Student: Class: Date: 1. Mr. Lopez has a rectangular classroom that measures 36
More information1 8 Practice Perimeter Circumference And Area Form K Answers
1 8 Practice Perimeter Circumference And Area Form K Answers We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer,
More informationPythagorean Theorem Name:
Name: 1. A wire reaches from the top of a 13-meter telephone pole to a point on the ground 9 meters from the base of the pole. What is the length of the wire to the nearest tenth of a meter? A. 15.6 C.
More information9.3 Altitude-on-Hypotenuse Theorems
9.3 Altitude-on-Hypotenuse Theorems Objectives: 1. To find the geometric mean of two numbers. 2. To find missing lengths of similar right triangles that result when an altitude is drawn to the hypotenuse
More informationTwo Special Right Triangles
Page 1 of 7 L E S S O N 9.3 In an isosceles triangle, the sum of the square roots of the two equal sides is equal to the square root of the third side. Two Special Right Triangles In this lesson you will
More information1 8 Practice Perimeter Circumference And Area Answers Form G
1 8 Practice Perimeter Circumference And Area Answers Form G We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer,
More information25. [Perimeter] 4 2 = Measure each side length of the shape. Add together the side lengths.
25. [Perimeter] Skill 25.1 Finding the perimeter of polygons by measuring their side lengths. Measure each side length of the shape. Q. Use a ruler to find the perimeter of the scalene triangle in millimetres.
More informationName Date. 5. In each pair, which rational number is greater? Explain how you know.
Master 3.18 Extra Practice 1 Lesson 3.1: What Is a Rational Number? 1. Which of the following numbers are equal to? 2. Write the rational number represented by each letter as a decimal. 3. Write the rational
More informationChapter 7. Right Triangles and Trigonometry
Chapter 7 Right Triangles and Trigonometry 4 16 25 100 144 LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor 8 20 32 = = = 4 *2 = = = 75 = = 40 = = 7.1 Apply the Pythagorean Theorem Objective:
More informationAdditional Exercises 3.1
Additional Exercises 3.1 Express the statement as an algebraic expression. 1. Fifteen divided by a number x. 1. 2. The difference between a number x and 50 2. 3. The cost C decreased by 14% 3. 4. The profit
More informationParking Lot HW? Joke of the Day: What do you call a leg that is perpendicular to a foot? Goals:
Parking Lot Joke of the Day: HW? What do you call a leg that is perpendicular to a foot? a right ankle Goals: Agenda 1 19 hw? Course Recommendations Simplify Radicals skill practice L8 2 Special Right
More informationChapter Test Form B 11
CHAPTER TEST FORM B 11 PDF - Are you looking for chapter test form b 11 Books? Now, you will be happy that at this time chapter test form b 11 PDF is available at our online library. With our complete
More informationPractice A. Congruent Figures. Are there any congruent figures in each picture? If there are, describe them
Name Date Class Practice A Are there any congruent figures in each picture? If there are, describe them. Determine the unknown measure in each set of congruent polygons. 7. 8. 9. 10. Name Date Class Practice
More informationMORE TRIGONOMETRY
MORE TRIGONOMETRY 5.1.1 5.1.3 We net introduce two more trigonometric ratios: sine and cosine. Both of them are used with acute angles of right triangles, just as the tangent ratio is. Using the diagram
More informationSum Fun Tournament Meeting (Multiple Topics)
Sum Fun Sum Fun Tournament Meeting (Multiple Topics) Sum Fun Topic There are a wide range of topics and difficulty levels covered during this meeting. Materials Needed The first four items listed below
More informationEQ: GPE.4 How do I calculate distance, midpoint, and slope?
EQ: GPE.4 How do I calculate distance, midpoint, and slope? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 3,
More informationPerimeter. Name. 22 Topic 17. Reteaching Find the perimeter of the figure below.
Perimeter Reteaching 1-1 Find the perimeter of the figure below. 15 m x 4 ft 4 ft 2 ft y 2 ft 5 ft 6 m 20 ft Reteaching 1-1 By using a formula: There are two equal lengths and equal widths, so you can
More informationBishop Kelley High School Summer Math Program Course: Trigonometry and Trigonometry with Pre-Calculus
015 01 Summer Math Program Course: Trigonometr and Trigonometr with Pre-Calculus NAME: DIRECTIONS: Show all work on loose-leaf paper, which ou will turn in with the packet. (NO WORK IN PACKET!) Put final
More informationStudent Outcomes. Lesson Notes. Classwork. Discussion (20 minutes)
Student Outcomes Students explain a proof of the converse of the Pythagorean Theorem. Students apply the theorem and its converse to solve problems. Lesson Notes Students had their first experience with
More information{Recall that 88 ft = 60 mi so 88 ft x h = 1 s h s 60 mi General Atomics Sciences Education Foundation All rights reserved.
Simulation Tool Development 1. a. Develop a scale model car tat sows te distance traveled in 1 s at speeds from 10 to 70 mp in increments of 10 mp. Use a scale of 1 in = 100 ft. Include a marker on eac
More informationApplication of Geometric Mean
Section 8-1: Geometric Means SOL: None Objective: Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse
More informationLesson 21: Special Relationships within Right Triangles Dividing into Two Similar Sub-Triangles
: Special Relationships within Right Triangles Dividing into Two Similar Sub-Triangles Learning Targets I can state that the altitude of a right triangle from the vertex of the right angle to the hypotenuse
More informationGeometry Chapter 7 Review Right Triangles Use this review to help prepare for the Chapter 7 Test. The answers are attached at the end of the document.
Use this review to help prepare for the hapter 7 Test. The answers are attached at the end of the document. 1. Solve for a and b. 2. Find a, b, and h. 26 24 a h b 10 b a 4 12. The tangent of is. 4. A is
More informationGeometry 1A Multiple Choice Final Exam Practice
Name Date: Per: Geometry 1 Multiple hoice Final Eam Practice 1. Let point E be between points F and G. Solve for r. FE = 6r 20 EG = 5r 24 FG = 55 [] r = 14 [] r = 5 [] r = 4 [D] r = 9 2. m JHI = ( 2 7)
More informationCH 21 THE PYTHAGOREAN THEOREM
121 CH 21 THE PYTHAGOREAN THEOREM The Right Triangle A n angle of 90 is called a right angle, and when two things meet at a right angle, we say they are perpendicular. For example, the angle between a
More informationName. STAR CITY Math / Geometry / Review: Right Triangles. Teacher Period
STAR CITY Math / Geometry / Review: Right Triangles 1. Firefighters use a 20 foot extension ladder to reach 16 feet up a building. How far from the building should they place the base of the ladder? Name
More informationDo not turn this page until you are asked to.
YEAR 7 MATHEMATICS EXAMINATION SEMESTER 2 2016 QUESTION AND ANSWER BOOKLET STUDENT NAME: TEACHER: DATE: TIME ALLOWED FOR THIS PAPER Reading time before commencing work: 10 minutes Working time for this
More information84 Geometric Mean (PAAP and HLLP)
84 Geometric Mean (PAAP and HLLP) Recall from chapter 7 when we introduced the Geometric Mean of two numbers. Ex 1: Find the geometric mean of 8 and 96.ÿ,. dÿ,... : J In a right triangle, an altitude darn
More informationWeek 8, Lesson 1 1. Warm up 2. ICA Scavanger Hunt 3. Notes Arithmetic Series
CAN WE ADD AN ARITHMETIC SEQUENCE? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 8, Lesson 1 1. Warm up 2. ICA
More informationDIRECTIONS FOR GEOMETRY CONSTRUCTION PROJECT
Name Period DIRECTIONS FOR GEOMETRY CONSTRUCTION PROJECT Materials needed: Objective: Standards: 8 pieces of unlined white computer paper (8.5 in. by 11in.), compass, ruler, protractor, pencil, and markers/colored
More informationRegional winter Tournament Saint Nicholas Thaumaturge - Bourgas
Regional winter Tournament Saint Nicholas Thaumaturge - Bourgas Area: Mathematics and Information Technologies Style of the Competition: Test exam with multiple-choice and free answers and a problem for
More informationCCM8 Unit 7: Pythagorean Theorem Vocabulary
CCM8 Unit 7: Pythagorean Theorem Vocabulary Base Exponent Hypotenuse Legs Perfect Square Pythagorean Theorem When a number is raised to a power, the number that is used as a factor The number that indicates
More information11.4 Apply the Pythagorean
11.4 Apply the Pythagorean Theorem and its Converse Goal p and its converse. Your Notes VOCABULARY Hypotenuse Legs of a right triangle Pythagorean theorem THE PYTHAGOREAN THEOREM Words If a triangle is
More informationPOST TEST KEY. Math in a Cultural Context*
Fall 2007 POST TEST KEY Building a Fish Rack: Investigation into Proof, Properties, Perimeter and Area Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: POST TEST KEY Grade: Teacher:
More informationChapter 8: Right Triangles (page 284)
hapter 8: Right Triangles (page 284) 8-1: Similarity in Right Triangles (page 285) If a, b, and x are positive numbers and a : x = x : b, then x is the between a and b. Notice that x is both in the proportion.
More informationBASICS OF TRIGONOMETRY
Mathematics Revision Guides Basics of Trigonometry Page 1 of 9 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier BASICS OF TRIGONOMETRY Version: 1. Date: 09-10-015 Mathematics Revision
More informationA life not lived for others is not a life worth living. Albert Einstein
life not lived for others is not a life worth living. lbert Einstein Sides adjacent to the right angle are legs Side opposite (across) from the right angle is the hypotenuse. Hypotenuse Leg cute ngles
More informationLesson 3: Using the Pythagorean Theorem. The Pythagorean Theorem only applies to triangles. The Pythagorean Theorem + = Example 1
Lesson 3: Using the Pythagorean Theorem The Pythagorean Theorem only applies to triangles. The Pythagorean Theorem + = Example 1 A sailboat leaves dock and travels 6 mi due east. Then it turns 90 degrees
More information7.4 Special Right Triangles
7.4 Special Right Triangles Goal p Use the relationships among the sides in special right triangles. Your Notes The etended ratio of the side lengths of a --908 triangle is 1:1: Ï 2. THEOREM 7.8: --908
More informationSection 8: Right Triangles
The following Mathematics Florida Standards will be covered in this section: MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition
More information4-7 The Law of Sines and the Law of Cosines
Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. 27. ABC, if A = 42, b = 12, and c = 19 Use the Law of Cosines to find the missing side measure. Use
More informationName: Period: Unit 5 Test Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Period: Unit 5 Test Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measures and. 6.4 2.3 2. Given that bisects and, find. Y Z W 3.
More informationDeriving the Law of Cosines
Name lass Date 14. Law of osines Essential Question: How can you use the Law of osines to find measures of any triangle? Resource Locker Explore Deriving the Law of osines You learned to solve triangle
More informationUnit 4. Triangle Relationships. Oct 3 8:20 AM. Oct 3 8:21 AM. Oct 3 8:26 AM. Oct 3 8:28 AM. Oct 3 8:27 AM. Oct 3 8:27 AM
Unit 4 Triangle Relationships 4.1 -- Classifying Triangles triangle -a figure formed by three segments joining three noncollinear points Classification of triangles: by sides by angles Oct 3 8:20 AM Oct
More information21st AMC (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
21st AMC 8 2005 2 1. Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer? (A) 7.5 (B) 15 (C)
More informationCH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES
CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES 317 Recalling The Pythagorean Theorem a 2 + b 2 = c 2 a c 90 b The 90 angle is called the right angle of the right triangle. The other two angles of the right
More informationChoose the correct answer. For Games Day, 112 students were organized into teams of 8. How many teams were formed? 12
Choose the correct answer. Page For Games Day, students were organized into teams of. How many teams were formed? 4 9 Ace Sporting Goods displays boxes of basketballs. They have 7 boxes. They want to make
More informationUnit 7. Math Problem 1. This segment will go through the endpoint of the original line segment, perpendicular to the line segment.
Math 1007 Unit 7 1 Construct a square with sides equal to r. 1: Extend the segment and draw a circle centered at one of the endpoints of the segment 2: Draw two larger congruent circles centered where
More informationSpecial Right Triangle Task Cards
Special Right Triangle Task Cards 45-45-90 and 30-60-90 Special Right Triangle Task Cards 45-45-90 and 30-60-90 Teachers: I have included 2 sets of task cards. The first set (slides 3-9) asks for the answer
More informationLength, Perimeter & Area
St Andrew s Academy Mathematics Department S BLOCK Length, Perimeter & Area Name : Score : Line Segment - Ruler Centimeter: S1 Measure the length of each line segment. 1) cm ) cm 3) cm 4) cm 5) cm Draw
More informationFirst Name: Last Name: Student scores will be sent to the address you provide above.
Mathworks Math Contest For Middle School Students October 14, 2014 PROCTORING TEACHER COVER SHEET! Please complete the following fields and return this cover sheet with all student exams! Only one Proctoring
More informationSimplifying Radical Expressions and the Distance Formula
1 RD. Simplifying Radical Expressions and the Distance Formula In the previous section, we simplified some radical expressions by replacing radical signs with rational exponents, applying the rules of
More informationPerimeter. Perimeter is the distance around a shape. You can use grid. Step 1 On grid paper, draw a rectangle that has a length
Lesson 13.1 Perimeter Perimeter is the distance around a shape. You can use grid paper to count the number of units around the outside of a rectangle to find its perimeter. How many feet of ribbon are
More informationA B
Bicentennial Olympiad Qualifying Round PROBLEM ONE The figure at the right is a magic square with missing entries. When complete, the sum of the four entries in each column, each row, and each diagonal
More informationCumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.
Name Score Math Course 1 1B 1. Use the numbers 5, 11, and 16 to make two addition facts and two subtraction facts. 11 + 12 12 + 12 12 12 12 12 2. Use the numbers 4, 16, and 64 to make two multiplication
More informationTest Review: Geometry I Period 2,4,6. TEST DATE: All classes Wednesday April 9. Things it would be a good idea to know:
Test Review: Geometry I Period 2,4,6 TEST DATE: All classes Wednesday April 9 Things it would be a good idea to know: 1) Special Right Triangles 2) Geometric Mean 3) SOHCAHTOA Test Outline Part I - Non-Calculator
More informationCumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.
Name Score Math Course 1 1A 1. Use the numbers 6, 12, and 18 to make two addition facts and two subtraction facts. 12 + 12 12 + 12 12 12 12 12 2. Use the numbers 5, 15, and 75 to make two multiplication
More informationPractice Test. 2 What is the area of this figure?
Practice Test 1 Which letter has a line of symmetry? S J R W L 3 Jane's house has a garden which is in the shape of a square. If each side of the garden is 18 feet then what is the perimeter of the garden?
More information5.5 Use Inequalities in a Triangle
5.5 Use Inequalities in a Triangle Goal p Find possible side lengths of a triangle. Your Notes Example 1 Relate side length and angle measure Mark the largest angle, longest side, smallest angle, and shortest
More informationROUND TOSS-UP: What is the square root of one million? (1000) (10 points) BONUS: How many zeros are at the end of ?
ROUND 1 1. TOSS-UP: What is 24% of 50? (12) (10 points) BONUS: A clothing store is having a 60% off sale on its dresses. Brandi has a coupon that lets her take 20% off of the sale price. If she pays $24
More informationParallel Lines Cut by a Transversal
Name Date Class 11-1 Parallel Lines Cut by a Transversal Parallel Lines Parallel Lines Cut by a Transversal A line that crosses parallel lines is a transversal. Parallel lines never meet. Eight angles
More informationFurman University Wylie Mathematics Tournament Ciphering Competition. March 10, 2007
Furman University Wylie Mathematics Tournament Ciphering Competition March 10, 2007 House Rules 1. All answers are integers(!) 2. All answers must be written in standard form. For example, 8 not 2 3, and
More informationTranslations: Comparison Sentences
Translations: Comparison Sentences A comparison sentence is a special form of translation, a single sentence within a word problem that provides information about two different things: two unknowns. In
More informationB.U.G. Newsletter. Full Steam Ahead! September Dr. Brown
B.U.G. Newsletter September 2014 THIS NEWSLETTER IS A SERVICE THAT WAS FUNDED BY "NO CHILD LEFT BEHIND" TITLE II PART A HIGHER EDUCATION IMPROVING TEACHER QUALITY HIGHER EDUCATION GRANT ADMINISTERED THROUGH
More informationNON-CALCULATOR Page Page , 31
Math 7 Midterm Review Please Note: Some topics covered in semester 1 are not found in our textbook. Therefore, the following topics are NOT covered in this review guide but WILL be on the exam. Refer to
More information13.7 Quadratic Equations and Problem Solving
13.7 Quadratic Equations and Problem Solving Learning Objectives: A. Solve problems that can be modeled by quadratic equations. Key Vocabulary: Pythagorean Theorem, right triangle, hypotenuse, leg, sum,
More informationMixed Trig Problems. For each problem show a complete solution with diagrams that include all the pertinent facts and answers.
Mixed Trig Problems For each problem show a complete solution with diagrams that include all the pertinent facts In ABC, cos A = 0.6. Find sin A and tan A. In ABC, cos A = 0.6. Find sin A and tan A. Sin
More informationChapter. Similar Triangles. Copyright Cengage Learning. All rights reserved.
Chapter 5 Similar Triangles Copyright Cengage Learning. All rights reserved. 5.4 The Pythagorean Theorem Copyright Cengage Learning. All rights reserved. The Pythagorean Theorem The following theorem will
More informationTHE 2018 ROSENTHAL PRIZE for Innovation in Math Teaching. Geometry Project: DARTBOARD
THE 2018 ROSENTHAL PRIZE for Innovation in Math Teaching Geometry Project: DARTBOARD Geometric Probability Theoretical Probability and Experimental Probability Elizabeth Masslich Geometry grades 6-12 Table
More informationUnit 2 Day 4 Notes Law of Sines
AFM Unit 2 Day 4 Notes Law of Sines Name Date Introduction: When you see the triangle below on the left and someone asks you to find the value of x, you immediately know how to proceed. You call upon your
More informationParking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty?
Parking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty? a plane burger Agenda 1 23 hw? Finish Special Right Triangles L8 3 Trig Ratios HW:
More information