5.5 Vocabulary triangle rigidity included angle SSS Triangle Congruence HL Triangle Congruence

In Lesson 5-2, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent. The property of triangle rigidity gives you shortcuts for determining two triangles congruent. The first shortcut was SAS. A second is SSS: it states that if the side lengths of a triangle are given, the triangle can have only one shape.

Thus, if you have three sides of one triangle congruent to three sides of another then the triangles will be congruent. Again, this can be argued by the transformation congruence theorems. Thrm 5-8 Remember: The order of the letters is important

Example 1: Using SSS to Prove Triangle Congruence Use SSS to explain why ∆ABC  ∆DBC. Then, list the corresponding parts of the congruent triangles.

Example 2: Using SSS to Prove Triangle Congruence 2. Given: PN bisects MO, Isosceles Triangle PMO with base MO Prove: ∆MNP  ∆ONP Reasons Statements

In a right triangle there is a relationship between the legs and the hypotenuse known as the Pythagorean Theorem: a2 + b2 = c2 We will prove this in Ch 9. The Pythagorean Theorem can be used to prove the following: Thrm 5-9

Example 3A: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.

Check It Out! Example 3B Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If not, tell what else you need to know.

SSS or HL SSS or SAS Lesson Quiz: Part I Identify the theorem(s) that prove the triangles congruent. SSS or HL SSS or SAS

Lesson Quiz: Part II

HONORS: 1 2