Name: Period: Unit 5 Test Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 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 Given that bisects and, find. Y Z W

2 3. Each pair of suspension lines on a parachute are the same length and are equally spaced from the center of the chute. To turn, the sky diver shortens one of the lines. How does this help the sky diver turn? D a. Shortening one line moves the sky diver away from the perpendicular bisector of. This turns the sky diver toward the direction of the shortened line. b. Shortening one line moves the sky diver closer to the perpendicular bisector of. This turns the sky diver toward the direction of the shortened line. c. Shortening one line moves the sky diver away from the perpendicular bisector of. This turns the sky diver toward the direction of the longer line. d. Shortening one line moves the sky diver closer to the perpendicular bisector of. This turns the sky diver toward the direction of the longer line. 4. are the perpendicular bisectors of. Find Y 4.2 Z O a. = 4.2 c. = 7.4 b. = 3.4 d. = 14.8

3 5. Find the circumcenter of with vertices y x 2 3 a. (1, 1) c. b. (0, 0) d. 6. are the angle bisectors of and, respectively., and m. Find m. D O 40º a. m = c. m = b. m = d. m = 7. In,. Find. Y O Z a. = 2.2 c. = 3.3 b. = 1.1 d. = 3

4 8. The diagram shows a new kind of triangular bread. Where should the baker place her hand while spinning the dough so that the triangle is balanced? y x 9. Find the orthocenter of with vertices.

5 10. In, show that midsegment is parallel to and that. y (-4, 2) 2 K L x 2 (4, -2) (-4, -4) 4 a... The slope of. The slope of. The slopes are equal so. The length of. The length of.. b... The slope of. The slope of. The slopes are equal so. The length of. The length of.. c... The slope of. The slope of. The slopes are equal so. The length of. The length of.. d... The slope of. The slope of. The slopes are equal so. The length of. The length of..

6 11. Given with,, and, find the length of midsegment. = 6 Y = 5 3 a. Y = 3 c. Y = 2.5 b. Y = 1.5 d. Y = Vanessa wants to measure the width of a reservoir. She measures a triangle at one side of the reservoir as shown in the diagram. What is the width of the reservoir ( across the base)? 120 m 120 m 150 m 100 m Y 100 m a. 300 m c. 75 m b. 150 m d. 100 m

7 13. Write an indirect proof that an obtuse triangle does not have a right angle. Given: Prove: is an obtuse triangle. does not have a right angle. Let be an obtuse angle. ssume has a right angle. Let be a right angle. Use direct reasoning to lead to a contradiction. omplete the proof. [1] Sum of the interior s of a are Substitute for m. Subtract from both sides. [2] [3] dd to both sides. However, by the Protractor Postulate, a triangle cannot have an angle with a measure less than assumption that has a right angle is false. Therefore, does not have a right angle. a. [1] Triangle Inequality Theorem c. [1] Definition of an obtuse angle [2] Substitution Property of Inequality [2] Substitution Property of Inequality [3] [3] b. [1] Definition of an obtuse angle [2] Subtraction Property of Inequality [3] d. [1] Definition of an obtuse angle [2] Substitution Property of Inequality [3]. The 14. Write the sides of in order from shortest to longest. I 58º J K 62º 15. Tell whether a triangle can have sides with lengths 5, 11, and 7. a. Yes b. No

8 16. ompare m with m D 17. Danny and Dana start hiking from the same base camp and head in opposite directions. Danny walks 6 miles due west, then changes direction and walks for 5 miles to point. Dana hikes 6 miles due east, then changes direction and walks for 5 miles to point S. Use the diagram to find which hiker is farther from the base camp. 5 mi 140º 6 mi base camp 6 mi 130º R 5 mi a. Danny is farther from the base camp than Dana. b. Dana is farther from the base camp than Danny. c. oth hikers are the same distance from the base camp. d. There is not enough data to answer the question. S

9 18. Write a two-column proof. Given: Prove: D omplete the proof. Proof: Statements Given Reasons Reflexive Property of ongruence 3. [1] 3. ngle ddition Postulate [2] [3] a. [1] [2] omparison Property of Inequality [3] Hinge Theorem b. [1] [2] Hinge Theorem [3] omparison Property of Inequality c. [1] [2] omparison Property of Inequality [3] onverse of the Hinge Theorem d. [1] [2] onverse of the Hinge Theorem [3] omparison Property of Inequality 19. Find the value of x. Express your answer in simplest radical form. 5 x x a. c. x = b. x = d. x = x =

10 20. n architect designs the front view of a house with a gable roof that has a triangle shape. The overhangs are 0.5 meter each from the exterior walls, and the width of the house is 16 meters. What should the side length l of the triangle be? Round your answer to the nearest meter. l l 16 m 0.5 m 0.5 m a. 12 m c. 24 m b. 11 m d. 23 m 21. Find the values of x and y. Express your answers in simplest radical form º y 60º x a., c., b., d.,

11 Matching Match each vocabulary term with its definition. a. locus b. concurrent c. point of concurrency d. equidistant e. focus f. Pythagorean triple g. indirect proof 22. a set of points that satisfies a given condition 23. three or more lines that intersect at one point Match each vocabulary term with its definition. a. hypotenuse b. equidistant c. midsegment of a triangle d. altitude of a triangle e. leg of a triangle f. centroid of a triangle g. median of a triangle 24. the point of concurrency of the three medians of a triangle 25. a perpendicular segment from a vertex to the line containing the opposite side 26. a segment that joins the midpoints of two sides of the triangle 27. the same distance from two or more objects Match each vocabulary term with its definition. a. concurrent b. circumscribed c. incenter of a triangle d. circumference e. orthocenter of a triangle f. inscribed g. circumcenter of a triangle 28. the point of concurrency of the three altitudes of a triangle 29. the point of concurrency of the three angle bisectors of a triangle