REASONING WITH CONGRUENT TRIANGLES: LESSON 16

ROCK AND ROLL HALL OF FAME A glass pyramidal structure covers the interior exhibits. The front surface design of the “glass tent” is an isosceles triangle with a lattice framework.

OBJECTIVES: Understand congruence of figures as a special case of similarity of figures. Know and be able to use the four theorems providing sufficient conditions to prove triangles are congruent (SSS, SAS, AAS, ASA).

OBJECTIVES: Know and be able to use properties of the incenter, circumcenter and centroid of a triangle. Continue to develop the ability to write both synthetic and analytic arguments.

DEFINITIONS: Congruent triangles: Congruent triangles have the same size and shape, regardless of position or orientation.

SSS Congruence Theorem: If 3 sides of one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent.

SAS Congruence Theorem: If 2 sides and the included angle of one triangle are congruent to the corresponding sides and included angle of a second triangle, then the triangles are congruent.

ASA Congruence Theorem: If 2 angles and the included side of one triangle are congruent to the corresponding angles and included side of a second triangle, then the triangles are congruent.

AAS Congruence Theorem: If 2 angles and a nonincluded side of one triangle are congruent to the corresponding 2 angles and nonincluded side of a second triangle, then the triangles are congruent.

HL Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the 2 triangles are congruent. CPCTC: Corresponding Parts of Congruent Triangles are Congruent.

Let’s look at some examples of the SSS, SAS, ASA,AAS and HL Congruence Theorems: Pull out the notes that were given to you and let’s start with the Side-Side-Side Triangle Congruence Theorem.

Since you have seen the notes and the examples, let’s work out some problems together!! Pull out your worksheet on Similarity and Congruence from Unit 3 – Page 28 and Using Congruent Triangles: CPCTC from Practice 4-4.

Homework 6.1-More Congruent Triangles Worksheet You may work in groups!!