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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!!!!
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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)