Learning Target 7-5: Triangle Congruency Proofs.
Objective: Prove that two triangles are congruent using a two-column or flow
proof.
7-5
Example #1:
A. Use the following information to solve the two
column proof
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅
Given: 𝐴𝐵
̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐶𝐵
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐵𝐶𝐷
Statement:
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅
1. 𝐴𝐵
Reason:
1. Given
2.
2. Given
3.
3. Reflexive Property
4. ∆𝐴𝐵𝐷 ≅ ∆𝐵𝐶𝐷
4.
B. Develop a flow proof using your proof from part A.
Example #2:
A.) Use the following information to develop a
two-column proof.
̅̅̅̅ ∥ ̅̅̅̅
Given: 𝑃𝑄
𝑅𝑆
∠𝑃𝑅𝑄 ≅ ∠𝑆𝑄𝑅
Prove: ∆𝑃𝑄𝑅 ≅ ∆𝑆𝑅𝑄
Statement:
1. ∠𝑃𝑅𝑄 ≅ ∠𝑆𝑄𝑅
Reason:
1.
2.
2.
3.
3. Alternate Interior Angles are Congruent
̅̅̅̅ ≅ 𝑅𝑄
̅̅̅̅
4. 𝑅𝑄
4.
5. ∆𝑃𝑄𝑅 ≅ ∆𝑆𝑅𝑄
5.
B. Develop a flow proof using your proof from part A.
Example #3:
A. Develop a flow proof using the information below.
̅̅̅̅ ≅ ̅̅̅̅
Given: 𝑃𝑄
𝑅𝑆
∠𝑃𝑄𝑆 ≅ ∠𝑅𝑆𝑄
Prove: ∆𝑃𝑄𝑆 ≅ ∆𝑅𝑆𝑄
B. Develop a two-column proof using your proof from part A.
Example #4:
A.) Write a flow proof from the info below.
Given: ∠𝑁𝐸𝑅 ≅ ∠𝑁𝑉𝑅
̅̅̅̅
𝑅𝑁 bisects ∠𝐸𝑅𝑉
Prove: ∆𝐸𝑁𝑅 ≅ ∆𝑉𝑁𝑅
B. Develop a two-column proof using your proof from part A.
Example #5: Write a two-column proof
Given: ∠𝐵 ≅ ∠𝐷
̅̅̅̅ bisects𝐵𝐷
̅̅̅̅
𝐴𝐶
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐵𝐶
Statement:
1.
Reason:
1.
2.
2.
3.
3. Definition of Bisect
4.
4. Vertical Angles are Congruent
5. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐵𝐶
5.