AMSCO'S Geometry. New York - Rye High School

190 Congruence Based on Triangles2. In Corollary 5.1b, we proved that the median to the base of an isosceles triangle is also thealtitude to the base. If the median to a leg of an isosceles triangle is also the altitude to theleg of the triangle, what other type of triangle must this triangle be?Developing Skills3. Given: AEFB, AE > FB, DA > CB, 4. Given: SPR > SQT,PR > QTand A and B are right angles.Prove: SRQ STP and R TProve: DAF CBE and DF > CEDCSP QAEFBRT5. Given: DA > CB, DA ' AB, andCB ' AB6. Given: ABCD, BAE CBF,BCE CDF, AB > CDProve: DAB CBA and AC > BDProve: AE > BF and E FDCA B C DABE F7. Given: TM > TN, M is the midpoint of TR 8. Given: AD > CE and DB > EBand N is the midpoint of TS. Prove: ADC CEAProve: RN > SMBTD EM NRSACApplying SkillsIn 9–11, complete each required proof in paragraph format.9. Prove that the angle bisectors of the base angles of an isosceles triangle are congruent.10. Prove that the triangle whose vertices are the midpoints of the sides of an isosceles triangleis an isosceles triangle.11. Prove that the median to any side of a scalene triangle is not the altitude to that side.