AMSCO'S Geometry. New York - Rye High School

Chapter Summary 16712. C13. D C 14.SRAMBABPQ15. If two sides and the angle opposite one of those sides in a triangle are congruent to the correspondingsides and angle of another triangle, are the two triangles congruent? Justify youranswer or draw a counterexample proving that they are not.(Hint: Could one triangle be an acute triangle and the other an obtuse triangle?)Applying Skills16. Given: AEB bisects CED, AC ' CED, and BD ' CED.Prove: EAC EBD17. Given: ABC is equilateral, D is the midpoint of AB.Prove: ACD BCD18. Given: Triangle PQR with S on PQ and RS ' PQ; PSR is not congruent to QSR.Prove: PS QS19. Gina is drawing a pattern for a kite. She wants it to consist of two congruent triangles thatshare a common side. She draws an angle with its vertex at A and marks two points, B andC, one on each of the rays of the angle. Each point, B and C, is 15 inches from the vertex ofthe angle. Then she draws the bisector of BAC, marks a point D on the angle bisector anddraws BD and CD. Prove that the triangles that she drew are congruent.CHAPTER SUMMARYDefinitionsto Know• Adjacent angles are two angles in the same plane that have a commonvertex and a common side but do not have any interior points in common.• Complementary angles are two angles the sum of whose degree measuresis 90.• Supplementary angles are two angles the sum of whose degree measures is180.•A linear pair of angles are two adjacent angles whose sum is a straightangle.• Vertical angles are two angles in which the sides of one angle are oppositerays to the sides of the second angle.