Geometry Chapter 5 Review

Transcription

1 Geometry Chapter 5 Review Name Multiple Choice Identify the choice that best completes the statement or answers the question. 5. Point A is the incenter of. Find AS. 1. The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is _?_. twice as long one third as long half as long the same length 2. If and are all midsegments, find x Given the inscribed circle with center K, which statement can you not conclude? If is the perpendicular bisector of,find RS. 7. The point of concurrency of the three medians of a triangle is called the _?_ of the triangle. tri-sector point median point centrino centroid 8. If point P is the centroid of, find CP. 4. By the Concurrency of Perpendicular Bisectors Theorem, if, and are perpendicular bisectors, then _?_ Which is the longest side of? cannot be determined

2 10. Which is a possible value of x? 15. If is the perpendicular bisector of, find UV Using the Hinge Theorem and the diagram, you can conclude: 16. Which must be true given that C is the circumcenter of? none of these 12. Based on the diagram, which is a true statement? 17. Point M is the incenter of. Find MC. E is the midpoint of. 13. Triangle DEF is formed by connecting the midpoints of. The perimeter of is 24. What is the perimeter of? In the diagram,, and. Find GK Which method could have been used to inscribe the circle inside the triangle? Find the incenter P, then use PA as the radius. Find the incenter P, then use PQ as the radius. Find the circumcenter P, then use PA as the radius. Find the circumcenter P, then use PQ as the radius. 19. Which statement is not always true? The medians of a triangle intersect inside the triangle. The altitudes of a triangle intersect inside the triangle. A median of a triangle intersects a vertex of the triangle. An altitude of a triangle intersects a vertex of the triangle

3 20. Given that P is the centroid of, find PD. Short Answer In and. Write an inequality to show all possible values for QR. 26. In and. Write an inequality to show all the possible values for SR. 27. G is the centroid of and. Find the perimeter of. 21. In and. Which list gives the sides in order from shortest to longest? 22. Which can be the measures of the sides of a triangle? 3 cm, 4 cm, 7 cm 4 cm, 6 cm, 8 cm 5 cm, 5 cm, 12 cm 6 cm, 7 cm, 15 cm 23. Given that L is the midpoint of, which can be concluded from the diagram? 28. Point A is the centroid of. Find the perimeter of. 29. A campground has a convenience store located 100 yards due south of the shower facilities. There is a game room 100 yards due east of the convenience store. Camper A leaves the game room for the shower. What is the shortest travel distance possible? Camper B is doing laundry half way between the game room and the convenience store. Find the shortest distance Camper B can travel to get to the pool located half way between the store and the shower. 24. By the Hinge Theorem, which inequality gives the correct restriction on x? Camper C is lost, standing at the convenience store facing west. If his tent is equidistant from the store, the shower, and the game room, provide two-step instructions to get Camper C back to the tent. 30. A cargo ship travels due north from a port at a rate of 15 miles per hour while a cruise ship leaves the port at the same time, traveling due east at 20 miles per hour. Both ships stop after three hours. What is the shortest distance between the ships? Explain. There is an island 45 miles due north of the cargo ship and another island 60 miles due east of the cruise ship. Explain how the answer from part (a) can be used to find the shortest distance between the islands. A sailboat is equidistant from the two islands and the port. What is the shortest distance between the sailboat and the cargo ship? the sailboat and the port? the sailboat and the cruise ship?

4 Geometry Chapter 5 Review Answer Section MULTIPLE CHOICE 1. B 2. D 3. B 4. C 5. A 6. A 7. D 8. B 9. A 10. B 11. C 12. A 13. C 14. D 15. C 16. A 17. C 18. B 19. B 20. A 21. D 22. B 23. A 24. B SHORT ANSWER yd By the Pythagorean Theorem,, so and. By the Midsegment Theorem, because the pool and laundry room are midpoints, the distance from the laundry room to the pool is half the distance from the game room to the shower. Turn clockwise and walk forward 70.7 yards. 30. By the Pythagorean Theorem, the distance is miles. The islands and the port form a triangle where the ships current locations are midpoints of two sides, making the shortest path between the ships a midsegment of the triangle. The shortest distance between the islands is parallel to this side and twice as long, so the distance is 150 miles. 60 miles; 75 miles; 45 miles

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