EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem

Write a proof.

SOLUTION

Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram.

GIVEN WY XZ, WZ ZY, XY ZY

PROVE WYZ XZY

STATEMENTS REASONS

EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem

1. WY XZ 1. Given

4. 4. Definition of a right triangle

WYZ and XZY are right triangles.

L ZY YZ5. 5. Reflexive Property of Congruence

6. WYZ XZY 6. HL Congruence Theorem

3. 3. Definition of linesZ and Y are right angles

2. 2. WZ ZY, XY ZY Given

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.

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 BC CB5. 5. Reflexive Property of Congruence

6. ACB DBC 6. HL Congruence Theorem

GUIDED PRACTICE for Examples 3 and 4

4.

Use the diagram at the right.

Use the information in the diagram to prove that ACB DBC

STATEMENTS REASONS

1. AC DB 1. Given

2. 2. AB BC, CD BC Given

4. 4. Definition of a right triangle

ACB and DBC are right triangles.

3. 3. Definition of linesC B