EXAMPLE 3 Use the HypotenuseLeg Congruence Theorem Write

EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof. GIVEN PROVE WY XZ, WZ WYZ ZY, XY ZY XZY SOLUTION Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram.

EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem STATEMENTS 1. WY REASONS 1. Given XZ 2. WZ ZY, XY ZY 3. 4. lines Z and Y are right angles WYZ and XZY are 4. Definition of a right triangles. L 5. ZY 6. 2. Given 3. Definition of WYZ 5. Reflexive Property of Congruence YZ XZY 6. HL Congruence Theorem

EXAMPLE 4 Choose a postulate or theorem Sign Making You are making a canvas sign to hang on the triangular wall over the door to the barn shown in the picture. You think you can use two identical triangular sheets of canvas. You know that RP QS and PQ PS. What postulate or theorem can you use to conclude that PQR PSR?

EXAMPLE 4 Choose a postulate or theorem SOLUTION You are given that PQ PS. By the Reflexive Property, RP RP. By the definition of perpendicular lines, both RPQ and RPS are right angles, so they are congruent. So, two sides and their included angle are congruent. ANSWER You can use the SAS Congruence Postulate to conclude PQR PSR. that

GUIDED PRACTICE for Examples 3 and 4 Use the diagram at the right. 3. Redraw ACB and DBC side by side with corresponding parts in the same position.

GUIDED PRACTICE for Examples 3 and 4 STATEMENTS REASONS L 5. BC 5. Reflexive Property of Congruence 6. ACB CB DBC 6. HL Congruence Theorem

GUIDED PRACTICE for Examples 3 and 4 Use the diagram at the right. 4. Use the information in the diagram to ACB DBC prove that STATEMENTS 1. AC DB 2. AB BC, CD BC REASONS 1. Given 2. Given 3. Definition of 3. C 4. ACB and DBC are 4. Definition of a right triangles. B lines