Geometry CC 4.5 Overlapping Triangles
Page 17
Proving overlapping triangle to be congruent:
 Identify the shared parts of the two triangles (congruent through the Reflexive Property of Congruence).
 Separate triangles and mark up congruent parts using the Givens.
 Identify a strategy for proving the the triangles congruent.
Example 1: Given: ∠1 ≅ ∠2, ̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝐷𝐵
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵
Strategy for proving triangle congruence:_____________________________
1. Given: ∠1 ≅ ∠2, ̅̅̅̅
𝐴𝐵 ⊥ ̅̅̅̅
𝐵𝐶 , ̅̅̅̅
𝐷𝐶 ⊥ ̅̅̅̅
𝐵𝐶
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵
Strategy for proving triangle congruence:_____________________________
̅̅̅̅ ≅ ̅̅̅̅
2. Given: ∠1 ≅ ∠2, 𝐴𝐷
𝐴𝐸
Prove: ∆𝐴𝐸𝐵 ≅ ∆𝐴𝐷𝐶
Strategy for proving triangle congruence:_____________________________
3. Given: ∠𝐷 ≅ ∠𝐶, ∠𝐷𝐴𝐵 ≅ ∠𝐶𝐵𝐴
Prove: ∆𝐴𝐷𝐵 ≅ ∆𝐵𝐶𝐴
Strategy for proving triangle congruence:_____________________________
Complete the following proofs.
4. Given: ̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅̅̅
𝐷𝐵𝐶 , ̅̅̅̅
𝐴𝐵 ⊥ ̅̅̅̅
𝐵𝐶 , ̅̅̅̅
𝐷𝐶 ⊥ ̅̅̅̅
𝐵𝐶
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅
5. Given: ∠𝐵 ≅ ∠𝐶, 𝐴𝐵
Prove: ∆𝐴𝐸𝐵 ≅ ∆𝐴𝐷𝐶
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
Page 18