5.5 Proving Triangle 5.5 Proving Triangle Congruence by SSSCongruence by SSSOBJ: Students will be able to use Side-Side-Side (SSS) Congruence Theorem and Hypotenuse-Leg (HL) Congruence Theorem.

Do NowDo Now

2.

a) Find b) Find the value of x.

A

Side-Angle-Side (SSS) Congruence Side-Angle-Side (SSS) Congruence TheoremTheorem If 3 sides of one triangle are congruent to 3 sides of another triangle, then they are congruent

Remember!Remember!Adjacent triangles share a side, so you can apply the Reflexive Property

Example 1: Use SSS to explain why Example 1: Use SSS to explain why ∆∆ABCABC ∆ ∆CDACDA..

Example 2: Determine if the Example 2: Determine if the triangles are congruent. triangles are congruent. Explain your reasoning. Explain your reasoning.

Terms:Terms:Hypotenuse: side opposite the

right angleLegs: In a right triangle, the

adjacent sides to the right angle

HL (Hypotenuse HL (Hypotenuse Leg)Leg)

If the hypotenuse and a leg of a

right triangle are congruent to the hypotenuse and a leg of another right triangle, then they are

congruent.

Example 3: Can you Example 3: Can you use HL ?use HL ?

Example 4: Show Example 4: Show the two angles are the two angles are

congruent.congruent.