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Geometry Name_____________________________ Notes: Overlapping Triangles (4-7) Date___________________ Congruence in Overlapping Triangles Essential Understanding: Sometimes you will see pictures involving _________________ triangles. You can sometimes use the congruent corresponding parts of one pair of triangles to prove another pair of triangles congruent. Overlapping triangles may have a common ______________ or a common _____________. You can make these problems easier by ___________________ the overlapping triangles. EX 1: Identifying Common Parts What common angle do ACD and ECB share? E A B D C The common angle is _______. EX 2: You Try!! What is the common side in ABD and DCA ? What is the common side in ABD and BAC B C A D Proofs 1. Given: ZXW YWX , Z ZWX YXW Statements Y 1. Prove: ZW YX W Reasons ZXW YWX , ZWX YXW X 2. 2. 3. 1. ZWX YXW 4. Reflexive Property 3. 4. 2. Given: CA CE , BA DE Prove: BX DX Statements Reasons C B X A D 1. CA CE , BA DE 1. 2. CAE CEA 2. 3. E 4. 3. Reflexive Property 4. SAS 5. ABE EDA 5. 6. BXA DXE 6. 7. 8. BXA DXE Given 7. 8.