CONGRUENT TRIANGLES First, let’s start with congruent polygons (general). What makes two polygons congruent? ALL of the parts of one polygon are congruent.

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Presentation transcript:

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

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: StatementsReasons 3.  M   O 3. Third Angles Theorem 4.ΔLMN  ΔPON 4. CPCTC 1. Given 1.

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)