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 square tile. Use a complete sentence to explain how you determined your answer. Simplify each radical expression completely.. You are building a triangular play area for your new puppy. You decide that the play area will have angle measures of 50 degrees and 40 degrees as shown in the following figure. 4. 60 5. 8 6. 45 a. Which side of the play area is the longest? b. Which side of the play area is the shortest? c. Explain how you determined your answers in parts (a) and (b). 7. 108 8. 1 5 1
Name: ID: C 9. 10. 3 3 6 13.. The legs of the isosceles triangle each measure 14 inches. Calculate the length of the hypotenuse. 11. A bird leaves its nest and flies two miles due north, then three miles due east, then four miles due north, and then five miles due east, finally reaching the ocean. How far is its nest from the ocean? Show all your work. 14. The perimeter of the square is 3 centimeters. Calculate the length of its diagonal. 1. A tree was planted 15.9 feet from a house and eventually grew to a height of 3 feet. During a particularly bad electrical storm, lightning struck the tree, causing the top of the tree to break off 6 feet above the ground. If the severed part of the tree is falling toward the house, will it hit the house? Use a complete sentence to explain your reasoning. 15. Calculate the value of a.
Name: ID: C 16. The length of a diagonal of the square is 36 centimeters. Calculate the length of each side. 19. The length of a diagonal of the square in the figure below is 60 inches. Calculate the perimeter of the figure. The figure is composed of a square and a semicircle. 17. The length of a diagonal of the square is 1 centimeters. Calculate the area. 0.. The length of the hypotenuse in the 30 60 90 triangle shown is 8 meters. Calculate the lengths of sides a and b. 18. Calculate the area of the figure below using the information given in the diagram. The figure is composed of a triangle and a semicircle. Use 3.14 for π. 1. The length of the side opposite the 30 angle is 5 feet. Calculate the lengths of sides b and c. 3
Name: ID: C. The length of the side opposite the 60 angle is 8 millimeters. Calculate the lengths of sides a and c 4. The length of the longer leg in the 30 60 90 triangle shown is miles. Calculate the length of the hypotenuse. 3. A broadcast antenna is situated on top of a tower. The signal travels from the antenna to your house so you can watch TV. The angle of elevation from your house to the tower measures 30 and the distance from your house to the tower is 500 feet. Calculate the height of the tower and the distance the signal travels. 5. The length of the shorter leg in the 30 60 90 triangle below is 13 meters. Calculate the length of the hypotenuse. 6. Calculate the perimeter of the trapezoid. 4
Name: ID: C 7. Calculate the area of the triangle. List the angles and sides of each triangle in order from least to greatest. Do not measure the angles or sides. 30. 8. Calculate the area of the trapezoid. 31. 9. A broadcast antenna is situated on top of a tower, and the signal travels from the antenna to your house so that you can watch TV. The angle of elevation from your house to the tower measures 30 and the distance from your house to the tower is 775 feet. Find the height of the tower and the distance the signal travels. 3. Triangle ABC with the following: m A = 7,m B = 119,and m C = 34 33. Triangle RST with the following: RS = 8 cm,st = 0 cm,and RT = 14 cm Determine whether it is possible to form a triangle using segments with the following measurements. Explain. 34. 14 inches, 1 inches, 7 inches 35. 6 feet, 10 feet, 18 feet 5
Name: ID: C 36.. millimeters, 7. millimeters, 5.1 millimeters Determine the measure of each lettered angle. Calculate the missing side lengths of each triangle. Round your answers to the nearest tenth. Show all your work and use a complete sentence in your answer. 37. 40. x = 38. 41. y = 4. z = Calculate the unknown side lengths in each triangle. Show all your work and use a complete sentence in your answer. Do not evaluate the radicals. 39. List the sides of the triangle shown in order from least to greatest length. 43. Kayleigh states that all pairs of angles that form a linear pair are also supplementary. Kaoni states that all pairs of angles that are supplementary also form a linear pair. Who is correct? Use complete sentences to justify your reasoning. 6
Name: ID: C Calculate the unknown side lengths in each triangle. Show all your work and use a complete sentence in your answer. Do not evaluate the radicals. 44. a = c = 45. b = c = 7
Geometry Chapter 4 Test Review Answer Section 1. ANS: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Angle PMU is an exterior angle of triangle PMB: m PMU = m PBM + m BPM = 35 + 1 = 56 The sum of the measures of the interior angles of a triangle is equal to 180 : m PMU + m MUP + m UPM = 180 56 + 6 + m UPM = 180 = 6 So, the measure of angle UPM is 6. PTS: 1 REF: Ch4.1 TOP: Assignment. ANS: a. The longest side of the play area is the side opposite the angle that is not labeled. b. The shortest side of the play area is the side opposite the 40-degree angle. c. First, determine the measure of the missing angle by the Triangle Sum Theorem. So, the measure of the missing angle is 180 (50 + 40 ) = 90. The longest side of a triangle is opposite the largest interior angle, and the shortest side of a triangle is opposite the smallest interior angle. So, the longest side is the side opposite the 90-degree angle and the shortest side is opposite the 40-degree angle. PTS: 1 REF: Ch4.1 TOP: Assignment 3. ANS: The length of the tile is 9 inches because 9 9 = 81. PTS: 1 REF: Ch4. TOP: Assignment 4. ANS: 60 = 4.15 = 15 PTS: 1 REF: Ch4. TOP: Assignment 5. ANS: 8 = 4.7 = 7 PTS: 1 REF: Ch4. TOP: Assignment 6. ANS: 45 = 9.5 = 3 5 PTS: 1 REF: Ch4. TOP: Assignment 1
7. ANS: 108 = 36.3 = 6 3 PTS: 1 REF: Ch4. TOP: Assignment 8. ANS: 15 = 1 5. 5 5 = 5 5 = 5 5 PTS: 1 REF: Ch4. TOP: Assignment 9. ANS: 3 = 3. = 3 4 = 3 PTS: 1 REF: Ch4. TOP: Assignment 10. ANS: 36 = 3 6. 6 6 = 3 6 36 = 3 6 6 PTS: 1 REF: Ch4. TOP: Assignment 11. ANS: d = 6 + 8 d = 36 + 64 d = 100 d = 10 miles = 6 PTS: 1 REF: Ch4. TOP: Assignment 1. ANS: Because the tree severs 6 feet from the ground, that leaves 17 feet of the tree to fall toward the house. If the house is only 15.9 feet away, the tree will hit the house. There is no need to use the Pythagorean Theorem to deduce this. PTS: 1 REF: Ch4. TOP: Assignment 13. ANS: The length of the hypotenuse is 14 or about 19.80 inches. PTS: 1 REF: Ch4.3 TOP: Assignment 14. ANS: side = 3 4 = 8 cm The diagonal is 8 or about 11.31 centimeters. PTS: 1 REF: Ch4.3 TOP: Assignment
15. ANS: The value of a is 1 = 1 meters. PTS: 1 REF: Ch4.3 TOP: Assignment 16. ANS: Each side is 36 5.46 centimeters. PTS: 1 REF: Ch4.3 TOP: Assignment 17. ANS: side = 1 Ê 1 ˆ area = = 7 cm Ë Á The area of the square is 7 square centimeters. PTS: 1 REF: Ch4.3 TOP: Assignment 18. ANS: area of triangle = 1 (1)(1) = 7 cm diameter of circle = 1 radius of circle = 6 cm cm area of semicircle = 1 π(6 ) = 36π cm Total area = 7 + 36π 185.04 cm PTS: 1 REF: Ch4.3 TOP: Assignment 19. ANS: s = 60 three sides = 180 circumference of semicircle = 1 Ê π 60 ˆ Ë Á = 30 π perimeter = 180 + 30 π 193.89 in. PTS: 1 REF: Ch4.3 TOP: Assignment 3
0. ANS: shorter leg: a = 8 a = 14 m longer leg: b = a 3 = 14 3 4.5 m 1. ANS: longer leg: b = a 3 = 5 3 8.66 ft hypotenuse: c = a = 10 ft. ANS: shorter leg: a 3 = b a 3 = 8 a = 8 3 a 4.6 mm Ê 8 ˆ hypotenuse: c = a = Ë Á 3 = 16 9.4 mm 3 3. ANS: Height of tower is the short leg. long leg short leg = = 500 88.68 feet 3 3 The height of the tower is about 88.68 feet. hypotenuse = short leg 577.36 feet The distance the signal travels is about 577.36 feet. 4. ANS: short leg = 3 1.70 hypotenuse = short leg 5.4 miles 5. ANS: hypotenuse = short leg = 13 = 6 meters 4
6. ANS: Form a 30 60 90 right triangle as shown. short leg = 14 6 = 4 cm hypotenuse = 4 = 8 cm perimeter = 14 + 6 + 8 + 8 = 36 cm 7. ANS: Split the triangle into two 30 60 90 triangles as shown. base = 0 height = 10 3 area = 1 (0)(10 3) = 100 3 or about 173. cm 8. ANS: height of the trapezoid = 8 or about 5.66 cm length of longer base = 6 + 8 or about 11.66 cm area of trapezoid 1 (11.66 + 6)(5.66) 49.98 cm 9. ANS: The height of the tower is the short leg. The short leg is equal to the long leg divided by 3, or 775 447.45 feet. So, the height of the tower is about 447.45 feet. The hypotenuse 3 is twice the length of the short leg or 447.45 = 894.9 feet. So, the signal travels a distance of about 894.9 feet. 30. ANS: D, C, B; BC, BD, DC PTS: 1 REF: Ch4.5 TOP: Assignment 31. ANS: R, Q, P; PQ, PR, QR PTS: 1 REF: Ch4.5 TOP: Assignment 5
3. ANS: A, C, B; BC, AB, AC PTS: 1 REF: Ch4.5 TOP: Assignment 33. ANS: T, S, R; RS, RT, ST PTS: 1 REF: Ch4.5 TOP: Assignment 34. ANS: No. The length of any side of a triangle must be less than the sum of the measures of the two other sides. The longest side is 1 inches and the sum of the two shorter sides is 14 + 7 = 1 inches, and 1 is not less than 1. PTS: 1 REF: Ch4.5 TOP: Assignment 35. ANS: Yes. The length of any side of a triangle must be less than the sum of the measures of the two other sides. The longest side is 6 feet and the sum of the two shorter sides is 10 + 18 = 8 feet, and 6 is less than 8. PTS: 1 REF: Ch4.5 TOP: Assignment 36. ANS: Yes. The length of any side of a triangle must be less than the sum of the measures of the two other sides. The longest side is 7. millimeters and the sum of the two shorter sides is. + 5.1 = 7.3 millimeters, and 7. is less than 7.3. PTS: 1 REF: Ch4.5 TOP: Assignment 37. ANS: 18 + 4 = c 34 + 576 = c 900 = c 30 = c The hypotenuse is 30 inches. PTS: 1 REF: Ch4. TOP: Pre Test 38. ANS: 10 + b = 0 100 + b = 400 b = 300 b 17.3 The longer leg is about 17.3 meters. PTS: 1 REF: Ch4. TOP: Pre Test 6
39. ANS: MP, HP, HM Angle H has a measure of 180 (64 + 67 ) = 49. The angles in order from least to greatest measure are H, M, and P. So, the sides opposite these angles MP, HP,and HM are in order from least to greatest. PTS: 1 REF: Ch4.5 TOP: Pre Test 40. ANS: x = 4 PTS: 1 REF: Ch4.1 TOP: Post Test 41. ANS: y = 64 PTS: 1 REF: Ch4.1 TOP: Post Test 4. ANS: z = 68 PTS: 1 REF: Ch4.1 TOP: Post Test 43. ANS: Kayleigh is correct. It is possible to have two angles that are not adjacent but are supplementary, such as 1 and is the diagram shown below. PTS: 1 REF: Ch4.1 TOP: Post Test 44. ANS: a = 8 in. c = 8 in. The length of each leg is 8 inches. The length of the hypotenuse is 8 inches. PTS: 1 REF: Ch4.3 TOP: Post Test 7
45. ANS: b = 4 3 yd c = 8 yd longer leg: b = a 3 = 4 3 hypotenuse: c = a = 8 The length of the longer leg is 4 3 yards. The length of the hypotenuse is 8 yards. PTS: 1 REF: Ch4.4 TOP: Post Test 8