AMSCO'S Geometry. New York - Rye High School

132 Proving Statements in Geometry8. ABCD is a line segment and B is the midpoint of AC. Which of the followingmust be true?(1) C is the midpoint of BD(3) AC CD(2) AB BC (4) AC BD AD9. The statements “AB BC” and “DC BC” are true statements. Whichof the following must also be true?(1) AB BC AC (3) B, C, and D are collinear(2) A, B, and C are collinear (4) AB DC10. Triangle LMN has exactly two congruent sides. Triangle LMN is(1) a right triangle. (3) an isosceles triangle.(2) a scalene triangle. (4) an equilateral triangle.Part IIAnswer all questions in this part. Each correct answer will receive 2 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.11. Give a reason for each step used in the solution of the equation.3x 7 13 Given12. Given: DE ' EFProve: DEF is a right triangle.7 7__________3x 6 __________x 2 __________Part IIIAnswer all questions in this part. Each correct answer will receive 4 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.13. Given: ABC with D a point on AB and AC AD DB.Prove: ABC is isosceles.14. PQR is a line segment. PQ 4a 3, QR 3a 2 and PR 8a 6. Is Qthe midpoint of PQR? Justify your answer.