congruent triangles first, let’s start with congruent polygons (general). what makes two polygons...

CONGRUENT TRIANGLES• First, let’s start with congruent polygons (general). What makes two

polygons congruent?

• ALL of the parts of one polygon are congruent to the corresponding parts of the other polygon.

• Parts: angles and sides

• What does corresponding mean?

CONGRUENT TRIANGLES• Two triangles are congruent if and only if their corresponding parts are

congruent.

• How else could we say these two triangles are congruent? (make a congruence statement)

Valid congruence statements for congruent polygons must list corresponding vertices in the same order!!!!

CPCTC• CPCTC: Corresponding Parts of Congruent Triangles are Congruent

• If two polygons are congruent, then their corresponding parts are congruent.• If corresponding parts of polygons are congruent, then the polygons are

congruent.

• We can use this to say triangles are congruent if all corresponding parts are congruent

CORRESPONDING PARTS CHECKS

CORRESPONDING PARTS CHECKS

CORRESPONDING PARTS CHECKS

CORRESPONDING PARTS CHECKS

THIRD ANGLES THEOREM

• Why does this make sense?

Prove That Two Triangles are Congruent

Write a two-column proof.

Prove: ΔLMN ΔPON

Prove That Two Triangles are Congruent

2. LNM PNO 2. Vertical Angles Theorem

Proof:Statements Reasons

3. M O

3. Third Angles Theorem

4. ΔLMN ΔPON

4. CPCTC

1. Given1.

DON’T FORGET WHAT YOU ALREADY KNOW!!!

HOMEWORK

• Page 260: #’s 23, 24 (be sure to use the diagrams)• Page 261: # 32• Page 262: #’s 39, 40, 41• Enrichment worksheet (Overlapping Triangles)• 4.3 Congruent Triangles worksheet (if we don’t finish)