AMSCO'S Geometry. New York - Rye High School

184 Congruence Based on Triangles(Continued)EA B C DStatementsReasons4. ABE and EBC are 4. If two angles form a linear pair,supplementary. DCE andthey are supplementary.ECB are supplementary.5. ABE DCE 5. The supplements of congruentangles are congruent.6. AB > CD6. Given.7. ABE DCE 7. SAS (steps 1, 5, 6).8. AE > DE8. Corresponding parts of congruenttriangles are congruent.ExercisesWriting About Mathematics1. Joel said that the proof given in Example 1 could have been done by proving thatACE DBE. Do you agree with Joel? Justify your answer.2. Abel said that he could prove that equiangular triangle ABC is equilateral by drawingmedian BD and showing that ABD CBD. What is wrong with Abel’s reasoning?Developing Skills3. In ABC, if AB > AC, mB 3x 15 and mC 7x 5, find mB and mC.4. Triangle RST is an isosceles right triangle with RS ST and R and T complementaryangles. What is the measure of each angle of the triangle?5. In equilateral DEF,mD 3x y,mE 2x 40, and mF 2y. Find x, y,mD,mE, and mF.6. Given: C not on DABE and 7. Given: Quadrilateral ABCD withCA > CBAB > CB and AD > CDProve: CAD CBEProve: BAD BCDDBABCACED