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Geometry Worksheet 5.1A Bisectors, altitudes, and medians Name ________________________ Per ___ Date __________________ 1. Name all the parts in the triangle. a. Median b. Angle Bisector c. Altitude d. Perpendicular Bisector 2. Name all the parts in the triangle. a. Median b. Angle Bisector c. Altitude d. Perpendicular Bisector 3. Name all the parts in the triangle. a. Median b. Angle Bisector c. Altitude d. Perpendicular Bisector 4. If E is the midpoint of AB , F is the midpoint of BC , and G is the midpoint of AC , Name each: a. The altitudes of ΔABC b. The medians of ΔABC 5. Underline the correct word or phrase to complete each sentence. a. Three or more lines that intersect at a common point are called (parallel/perpendicular/concurrent) lines. b. Any point on the perpendicular bisector of a segment is (parallel to/congruent to/equidistant from) the endpoints of the segment. c. A(n) (altitude/angle bisector/median/perpendicular bisector) of a triangle is a segment drawn from a vertex of a triangle perpendicular to the line containing the opposite side. 6. A. B. C. D. E. F. FJ is what type of segment? ______ Perpendicular Bisector Altitude Median Angle Bisector A and C All of the above. A 7. Given: AO is an altitude and angle bisector Prove: AO is a median 1. AO is an altitude 2. 3. 4. AO is an angle bisector 5. 6. 7. ΔCOA ≅ ΔBOA 8. 9. AO is a median 1. B C O 2. If altitude then Create right angles with opposite side. 3. 4. 5. If angle bisector then divides angle into two Congruent angles. 6. 7. 8. 9. 8. In the proof above, what type of triangle is ΔCAB ? 9. What in real life could you relate the word altitude to so that you could remember the meaning of the word better? JJJG 10. BD is the perpendicular bisector of AC . Find AC. 11. Find x and y, if DE is a median C 5x-6 D B 3x+8 A JJJG 12. Find x if MR bisects (NMP , m(1 = 6 x − 9 , and m( 2 = 4 x + 13 . M JJJG 13. Find x if MR bisects (NMP , m(1 = 5 x + 8 , and m( 2 = 8 x − 16 . N 2 R N 1 R M P 14. Solve for x. 1 2 P 15. Find AC. C x+8 (3x+3)° T x-9 A B BT is an al ti tud e