Congruence in Right Triangles Lesson 4-6 Additional Examples One student wrote “ CPA MPA by SAS” for the diagram below. Is the student correct? Explain. The diagram shows the following congruent parts. CA MA CPA MPA PA PA There are two pairs of congruent sides and one pair of congruent angles, but the congruent angles are not included between the corresponding congruent sides. The triangles are not congruent by the SAS Postulate, but they are congruent by the HL Theorem.

Congruence in Right Triangles Lesson 4-6 Additional Examples XYZ is isosceles. From vertex X, a perpendicular is drawn to YZ, intersecting YZ at point M. Explain why XMY XMZ.

Congruence in Right Triangles Lesson 4-6 Additional Examples Write a two–column proof. Given: ABC and DCB are right angles, AC DB Prove: ABC DCB Statements Reasons 1. ABC and  DCB are 1. Given right angles. 2. ABC and DCB are 2. Definition of a right triangle right triangles. 3. AC DB 3. Given 4. BC CB 4. Reflexive Property of Congruence 5. ABC DCB 5. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. (HL Theorem).