Recall that for real numbers a, b, and c are real numbers, if and , then . This is called **Transitive Property of Equality**. This is also the same with congruence. If , , and are polygons, and if is congruent to , and is congruent , then is congruent to . This is called the **Transitive Property of Congruence**. We will use this to prove the following problem.

Given: and .

Prove: .

**Proof**

It is given that .

Now, by reflexive property, that is a segment is congruent to itself, .

Notice that is the hypotenuse of and is the hypotenuse of . Since both are right triangles

are congruent by the **Hypotenuse Leg Theorem**.

Next, we prove that .

It is given that .

since they are both right angles.

Now, by reflexive property.

Therefore, by the** SAS Congruence Theorem**.

Now, since , and ,

by Transitive Property of Congruence.

This is what we want to prove.

*Reference: UCSMP, Geometry*