Chapter 5: Properties and Attributes of Triangles Review Packet

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1 Geometry B Name: Date: Block: Chapter 5: Properties and Attributes of Triangles Review Packet All work must be shown to receive full credit. Define the following terms: 1. altitude of a triangle 2. centroid of a triangle 3. circumcenter of a triangle 4. circumscribed 5. concurrent 6. equidistant 7. incenter of a triangle 8. inscribed 9. locus 10. median of a triangle 11. midsegment of a triangle 12. orthocenter of a triangle

2 13. point of concurrency 14. Pythagorean triple 15. A point that is the same distance from two or more objects is from the objects. 16. A is a segment that joins the midpoints of two sides of the triangle. 17. The point of concurrency of the angle bisectors of a triangle is the. 18. A is a set of points that satisfies a given condition. 19. Find the following measures: BC, BD, and AC. 20. Find the following measures: YX and YZ. 2

3 Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints. 21. A (-4, 5), B (6, -5) 22. X (3, 2), Y (5, 10) 23. Find the following measures: m FGT, m GTF, m GTH and HT. 24. Find the following measures: m MNP and m MVP. 25. DG, EG and FG are the perpendicular bisectors of ABC. Find the lengths of AG, GB and GE. If necessary, round to the nearest tenth. 3

4 26. PX, PY, and PZ are the perpendicular bisectors of GHJ. Find each length: GY, GP, GJ, PX, and PH. If necessary, round to the nearest tenth. 27. QS and RS are angle bisectors of PQR. Find the distance from S to PR. What are the measures of TSQ and RQT? 28. UA and VA are angle bisectors of UVW. Find each measure: the distance from A to UV, m WVA, and m UAT. T 29. In JKL, JP = 42 NQ = 12. Find JQ, QP, NL and QL. 4

5 30. In DEF, DB = 24.6, and EZ = Find each length: DZ, ZB, ZC, and EC. 31. Find each measure: NQ and m NQM. 32. Find each measure: BC, XZ, XC, m BCZ, m BAX, and m YXZ. 33. The vertices of GHJ are G (-4, -7), H (2, 5), and J (10, -3). V is the midpoint of GH, and W is the midpoint of HJ. Show that VW GJ and VW = ½GJ. (Remember to do midpoints of GH and HJ; slope of VW and GJ and distance of VW and GJ.) 5

6 34. Find the value of x. Give your answer in simplest radical form. 35. Find the missing side length. Tell if the sides form a Pythagorean triple. Explain. 36. Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 9, 12, 16 11, 14, , 3.6, 3.9 2, 3.7, 4.1 6

7 37. Find the values of the variables. Give your answers in simplest radical form. 38. Find the values of the variables. Give your answers in simplest radical form. 39. Find the values of the variables. Give your answers in simplest radical form. 40. Find the value of each variable. Round to the nearest inch. 7

8 41. Find the missing side length, round to the nearest tenth if necessary. Tell if the side lengths result in a Pythagorean triple. 42. An entertainment center is 40 inches wide and 15 inches high. Will a TV with a 50 inch diagonal fit in? Explain. 43. Justify if the measures can be the side lengths of the triangle. If so, classify the triangle as acute, obtuse or right. 15, 18, Justify if the measures can be the side lengths of the triangle. If so, classify the triangle as acute, obtuse or right. 7, 8, Justify if the measures can be the side lengths of the triangle. If so, classify the triangle as acute, obtuse or right 10, 24, 26 8

9 46. The planners for a new section of the city want every location on Main Street to be equidistant from Elm Street and Grove Street. How can the planners ensure that this is the case? 47. In each support for the garden swing, the crossbar DE is attached at the midpoints of legs BA and BC. The distance AC is 4 ½ feet. The carpenter has a timber that is 30 inches long. Is this timber long enough to be used as one of the crossbars? Explain. 48. The safety rules for a playground state that the height of the slide and the distance from the base of the ladder to the front of the slide must be in a ratio of 3 : 5. If a slide is about 8 feet long, what are the height of the slide and the distance from the base of the ladder to the front of the slide? Round to the nearest inch. 9

10 49. Using the picture a. Given that FH is the perpendicular bisector of EG, EF = 4b, and FG = 2b + 56, find FG. b. Given that EF = 10.2, EH = 6.7, and FG = 10.2, find EG. 50. In Triangle ABC, AE = 16, DG = 9, and BG = 12. Find each length. a. AG b. GC c. BF smilardo.wordpress.com - homework: worksheets: link to book and more Follow 10

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