4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To...

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.

• Corresponding sides are congruent

• Corresponding angles are congruent

Congruence Statement

When naming two congruent triangles, order is very important.

Example

Write a congruence statement for the congruent triangles below.

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 Theorem

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

Congruent Triangles

Checking 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 Postulate

SSS 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 Shortcuts

Side-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…?

Classwork

From 4.13 - 1232 – 3538 – 4046 – 48*

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