EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof. GIVEN WY XZ, WZ ZY, XY ZY PROVE WYZ 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 REASONS WY XZ Given WZ ZY, XY ZY Given Definition of lines Z and Y are right angles Definition of a right triangle WYZ and XZY are right triangles. L ZY YZ Reflexive Property of Congruence WYZ XZY 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 RPQ and RPS are right angles, so they are congruent. So, two sides and their included angle are congruent. You are given that PQ PS . By the Reflexive Property, RP RP . By the definition of perpendicular lines, both You can use the SAS Congruence Postulate to conclude that . PQR PSR ANSWER

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

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

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