4. 1 Apply Congruence and Triangles 4

4.1 Apply Congruence and Triangles4.2 Prove Triangles Congruent by SSS, SAS

Objectives:1. To define congruent triangles2. To write a congruent statement3. To prove triangles congruent by SSS,

SAS

Congruent Polygons

Congruent Triangles (CPCTC)Two triangles are congruent congruent

triangles triangles if and only if the ccorresponding pparts of those ccongruent ttriangles are ccongruent.

Congruence StatementWhen naming two congruent triangles,

order is very important.

Example Which polygon is congruent to ABCDE?

ABCDE -?-

Properties of Congruent Triangles

Example

What is the relationship between C and F?

30

30

75

75

E

F

D

A

C

B

Third Angle TheoremIf two angles of one triangle are

congruent to two angles of another triangle, then the third angles are also congruent.

Congruent TrianglesChecking to see if 3 pairs of

corresponding sides are congruent and then to see if 3 pairs of corresponding angles are congruent makes a total of SIX pairs of things, which is a lot! Surely there’s a shorter way!

Congruence Shortcuts? Will one pair of congruent sides be

sufficient? One pair of angles?

Congruence Shortcuts? Will two congruent parts be sufficient?

Congruent Shortcuts?Will three congruent parts be sufficient?

And if so….what three parts?

Investigation…… Using 2,3,4 Triangles

Side-Side-Side Congruence PostulateSSS Congruence Postulate:SSS Congruence Postulate:If the three sides of one triangle are

congruent to the three sides of another triangle, then the two triangles are congruent.

SSS Congruence Postulate

A B

C

D

Using a 2-Column Proof!Is ABC is

congruent to ABD? Why or why not?

Example Decide whether the triangles are

congruent. Explain your reasoning.

Investigation……

Part 2

Congruence ShortcutsSide-Angle-Side (SAS) Congruence Side-Angle-Side (SAS) Congruence

Postulate:Postulate:If two sides and the included angle of one

triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Can we prove?...yet?

What else would we need?

Can we Prove Triangle Congruence?

Another Proof…?

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