1. 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.

2. 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

3. 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?

4. 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

5. 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.

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

7. 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.