Entry Task Prove: <E + <H. 4.7 Overlapping Triangles Learning Target: I can identify congruent OVERLAPPING triangles Success Criteria: I can prove triangles.

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Presentation transcript:

Entry Task Prove: <E + <H

4.7 Overlapping Triangles Learning Target: I can identify congruent OVERLAPPING triangles Success Criteria: I can prove triangles congruent using overlapping parts. D E F G H

The triangles may have sides or angles in common. The best way to find the necessary parts is to : When triangles overlap it is sometimes difficult to see the corresponding congruent parts.

Separate and redraw  DFG &  EHG. Identify any shared parts. Example #1 D E F G H SHARED

Example #2 Separate and redraw  ACD &  BDC. Identify any shared parts. D C AB SHARED

Groups On a blank computer piece of paper, groups are to find the measure of each angle and justify that measure.

ASSIGNMENT: Homework: P. 268 #1-3, 6, 8-13,15 Challenge - Slide #6 (worth 1 point for each correct angle measure)

Given: CA CE, BA DE Write a two-column proof to show that  CBE  CDA. 3. CA = CE, BA = DE 3. Definition of congruent segments. 4. CA – BA = CE – DE 4. Subtraction Property of Equality 5. CA – BA = CB,5. Segment Addition Postulate CE – DE = CD 6. CB = CD6. Substitution Using Corresponding Parts of Congruent Triangles Plan:  CBE  CDA by CPCTC if CBE CDA. This congruence holds by SAS if CB CD. Proof: StatementsReasons 1.  BCE  DCA 1. Reflexive Property of Congruence 2. CA CE, BA DE 2. Given 7. CB CD7. Definition of congruence 8. CBE CDA8. SAS 9.  CBE  CDA9. CPCTC Quick Check Separating Overlapping Triangles

Example #3 GIVEN:  ZXW   YWX  ZWX   YXW PROVE:ZW  YX STATEMENTSREASONS X W ZY

STATEMENTSREASONS Example #4 GIVEN: CA  CE BC  DC PROVE: AD  BE A B C D X E