Test #7 Review. 8) In ABC, G is the centroid and BE = 15. Find BG and GE.

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1 ) Test #7 Review 1) Name the point of concurrency of the angle bisectors. (Note: Not all lines shown are angle bisectors.) 2) Name an altitude for MNO. 3) Name an median for. M P Q E ) ) ) O R N F For a triangle, match the respective names of the points of concurrency with the appropriate special segment: 4) Perpendicular isectors 5) ngle isectors 6) Medians 7) ltitudes a. entroid b. ircumcenter c. Incenter d. Orthocenter 8) In, G is the centroid and E = 15. Find G and GE. G F E

2 9) Which diagram shows a point of concurrency, point P, that is an equal distance from points,, and? a) c) b) d) 10) Find the length of, given that is a median of the triangle and = ) Find m ) Find. 13) Find x + 6 5x

3 14) Write an equation of the perpendicular bisector of the segment with endpoints G( 2, 0) and H(8, 6) and graph both lines. 15) In the diagram, bisects. Find. 6x + 3 3x ) Find the coordinates of the circumcenter of with vertices ( 5, 6), ( 7, 2), and ( 3, 2).

4 17) In, N is the incenter, N = 4x + 5, and NF = 7x 10. Find NE. F N E 18) In LMN, P is the centroid, and P = 3. Find LP and L. N P L M 19) company builds trusses to support structures. In the truss shown below, the support GH is the midsegment of. Find the value of x. H x ft G 21 ft

5 20) The Park and Recreation department wants to add some sidewalks to the park. The fountain F is located at the park s centroid and is 85 feet from entrance. How many feet of sidewalk are needed to connect the fountain to the gift shop? petting zoo F snack cart gift shop 21) You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need? K H 21 ft 17 ft G 19 ft 22) List the sides of from shortest to longest In #23 and 24, complete the following statements with <, >, or = using the given figures below. 23) m 1 m 2 24) 2 M N

6 25) In, N is the incenter, NE = 8x 9, and N = 3x + 6. Which of the measures are possible lengths of NG? (You can have more than one correct answer.) a) 18.5 F b) 15.0 c) 15.7 N E G d) ) triangle has one side that measures 1 foot and another side that measures 20 inches. Which are possible side lengths of the third side? (You can have more than one correct answer.) a) 13 in. b) 28 in. c) 6 in. d) 36 in. In #27 30, match the set of segment lengths below with its description. ) is the largest angle in. ) is the largest angle in. ) is the largest angle in. ) The segments do not form a triangle. 27) = 10, = 28, = 15 29) = 39, = 13, = 29 28) = 27, = 34, = 14 30) = 20, = 14, = 21

7 31) Find the coordinates of the centroid of with vertices (7, 2), (9, 3), and (5, 5). 32) Tell whether the orthocenter is inside, on, or outside the triangle with vertices Q( 7, 6), R( 7, 8), and S( 3, 8).Then find the coordinates of the orthocenter.

8 33) In, J and K are medians, JK = 10x 12, = 9x + 18, JM = 21, KM = 23, J = 60, and K = 52. J K M ) Find JK and. Round decimal answers to the nearest tenth. ) Find the perimeter of. ) Find the perimeter of M. 34) In the stained glass image, X Y, XF ZF, and YE. EZ omplete the below statements. ) E ) XY ) Y

9 Test #7 Review Test #7 Review: Points of oncurrency and Triangles nswer Section MULTIPLE HOIE 1. NS: PTS: 1 IF: L2 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Medians and ltitudes NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3 KEY: angle bisector incenter of the triangle point of concurrency 2. NS: PTS: 1 IF: L2 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Medians and ltitudes NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3 TOP: 5-3 Example 4 KEY: median of a triangle 3. NS: PTS: 1 IF: L3 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Medians and ltitudes NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3 KEY: angle bisector circumcenter of the triangle centroid orthocenter of the triangle median altitude perpendicular bisector 4. NS: PTS: 1 IF: L2 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Properties of isectors NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3 TOP: 5-3 Example 2 KEY: circumcenter of the triangle circumscribe 5. NS: PTS: 1 IF: L2 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Medians and ltitudes NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3 TOP: 5-3 Example 4 KEY: median of a triangle 6. NS: PTS: 1 IF: L2 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Medians and ltitudes NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3 TOP: 5-3 Example 3 KEY: centroid median of a triangle 7. NS: PTS: 1 IF: L2 REF: 5-3 oncurrent Lines, Medians, and ltitudes OJ: Medians and ltitudes NT: NEP 2005 G3b ST: TX TEKS G.2 TX TEKS G.3 TX TEKS G.3E TX TEKS G.9 TX TEKS G.2 TX TEKS G.3

10 Test #7 Review TOP: 5-3 Example 3 KEY: median of a triangle 8. NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.1 ST: G.6. KEY: perpendicular bisector NOT: Example 1 9. NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.1 ST: G.6. KEY: perpendicular bisector NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.1 ST: G.6. KEY: angle bisector NOT: Example NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.1 ST: G.2. G.6. KEY: perpendicular bisector NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.1 ST: G.6. KEY: angle bisector NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.2 NT: HSG-MG..1 HSG-MG..3 KEY: circumcenter NOT: Example NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.2 ST: G.6. KEY: incenter NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.3 ST: G.6. KEY: centroid NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.4 ST: G.5. G.6. KEY: midsegment of a triangle application NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.3 ST: G.6. KEY: centroid application NOT: pplication NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.4 ST: G.5. G.6. KEY: midsegment of a triangle application NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.5 ST: G.5. KEY: angles and sides of a triangle NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.6 ST: G.6. KEY: Hinge Theorem NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.6 ST: G.6. KEY: Hinge Theorem NOT: Example 2

11 MULTIPLE RESPONSE Test #7 Review 22. NS:, PTS: 1 IF: Level 2 REF: Geometry Sec. 6.2 ST: G.6. KEY: incenter NOT: Example NS:, PTS: 1 IF: Level 2 REF: Geometry Sec. 6.5 ST: G.5. KEY: side lengths of a triangle NOT: Example 5 MTHING 24. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.2 ST: G.6. KEY: incenter circumcenter NOT: ombined oncept 25. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.2 ST: G.6. KEY: incenter circumcenter NOT: ombined oncept 26. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.5 ST: G.5. KEY: angles and sides of a triangle NOT: ombined oncept 27. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.5 ST: G.5. KEY: angles and sides of a triangle NOT: ombined oncept 28. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.5 ST: G.5. KEY: angles and sides of a triangle NOT: ombined oncept 29. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.5 ST: G.5. KEY: angles and sides of a triangle NOT: ombined oncept SHORT NSWER 30. NS: PTS: 1 IF: Level 2 REF: Geometry Sec. 6.3 ST: G.6. KEY: centroid NOT: Example NS: on; PTS: 1 IF: Level 2 REF: Geometry Sec. 6.3 ST: G.5. G.6. KEY: orthocenter NOT: Example NS: a., b. about units c. about units

12 Test #7 Review PTS: 1 IF: Level 2 REF: Geometry Sec. 6.4 ST: G.2. G.6. KEY: midsegment of a triangle centroid NOT: ombined oncept 33. NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.4 ST: G.6. KEY: midsegment of a triangle application NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.4 ST: G.6. KEY: midsegment of a triangle application NOT: Example NS: PTS: 1 IF: Level 1 REF: Geometry Sec. 6.4 ST: G.6. KEY: midsegment of a triangle application NOT: Example 4