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Do Now • Are triangles ABC and DEF congruent? • A(-2,-2) B(4,-2) C(4,6) and D(5,7) E(5,1) F(13,1) – What types of lines make up the triangle? Congruence • How do we know if triangles are congruent? • What do we need to know about the triangles in order to be able to assume they are congruent? Side Angle Side Congruence Postulate • If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. Right Triangles • Can we assume that the triangles are congruent? Why? Hypotenuse Leg Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. Given: WY congruent to XZ, WZ perp. To ZY, and XY perp. To ZY Prove: Triangles WYZ and XZY are congruent • WY congruent to XZ • WZ perp. ZY, XY perp. ZY • Angles Z and Y are right • Triangles WYZ and XZY are right triangles • ZY congruent to YZ • Triangles WYZ and XZY are congruent. Given: WY congruent to XZ, WZ perp. To ZY, and XY perp. To ZY Prove: Triangles WYZ and XZY are congruent • WY congruent to XZ • WZ perp. ZY, XY perp. ZY • Angles Z and Y are right • Triangles WYZ and XZY are right triangles • ZY congruent to YZ • Triangles WYZ and XZY are congruent. • Given • Given • Def of Perpendicular • Def of a right Triangle • Reflexive Prop. Of Congruence • HL Congruence Thm