Entry Task 4.7 Overlapping Triangles G H F D Learning Target: •I can identify congruent OVERLAPPING triangles •Success Criteria: I can prove triangles congruent using overlapping parts. E When triangles overlap it is sometimes difficult to see the corresponding congruent parts. The triangles may have sides or angles in common. The best way to find the necessary parts is to : Example #1 Separate and redraw DFG & EHG. Identify any shared parts. G H F D E SHARED Example #2 Separate and redraw ACD & BDC. Identify any shared parts. A B C D SHARED Example #3 GIVEN: ZXW YWX Z ZWX YXW PROVE: ZW YX W STATEMENTS 1. 1. 2. 3. 4. 2. 3. 4. Y X REASONS Using Corresponding Parts of Congruent Triangles Separating Overlapping Triangles Given: CA CE, BA DE Write a two-column proof to show that CBE Plan: CBE CDA by CPCTC if CBE congruence holds by SAS if CB CD. Reasons Proof: Statements 1. BCE DCA 2. CA CE, BA DE 3. CA = CE, BA = DE 4. CA – BA = CE – DE 5. CA – BA = CB, CE – DE = CD 6. CB = CD 7. CB CD 8. CBE CDA 9. CBE CDA CDA. CDA. This 1. Reflexive Property of Congruence 2. Given 3. Definition of congruent segments. 4. Subtraction Property of Equality 5. Segment Addition Postulate 6. Substitution 7. Definition of congruence 8. SAS 9. CPCTC Quick Check Example #4 C GIVEN: CA CE BC DC B X PROVE: AD BE A STATEMENTS 1. 1. 2. 3. 4. 2. 3. 4. D E REASONS ASSIGNMENT: Homework: P. 268 #1-13,15,16, 20 Challenge - #20 Groups • On a blank computer piece of paper, groups are to find the measure of each angle and justify that measure.