Name ______________________________________________________
Date ___________________
Complete the following two-column proofs about congruent triangles.
Proof #1:
A
B
D
C
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅; 𝐴𝐷
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
Given: 𝐴𝐵
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵
Statements
Reasons
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ ; 𝐴𝐷
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
1. 𝐴𝐵
_______________________________________
̅̅̅̅ ≅ 𝐵𝐷
̅̅̅̅
2. 𝐵𝐷
_______________________________________
3. ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵
_______________________________________
M
A
Proof #2:
̅̅̅̅̅ ≅ 𝑇𝐻
̅̅̅̅ ; ∠𝑀𝐻𝑇 ≅ ∠𝐻𝑀𝐴
Given: 𝑀𝐴
Prove: ∆𝑀𝑇𝐻 ≅ ∆𝐻𝐴𝑀
Statements
T
H
Reasons
̅̅̅̅̅ ≅ 𝑇𝐻
̅̅̅̅ ; ∠𝑀𝐻𝑇 ≅ ∠𝐻𝑀𝐴
1. 𝑀𝐴
_______________________________________
2. ___________________________________
Reflexive property (same line)
3. ∆𝑀𝑇𝐻 ≅ ∆𝐻𝐴𝑀
_______________________________________
C
Proof #3:
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ ; L is the midpoint of 𝑂𝐷
̅̅̅̅
Given: 𝐶𝑂
Prove: ∆𝐶𝑂𝐿 ≅ ∆𝐶𝐷𝐿
Statements
O
L
D
Reasons
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ ; L is the midpoint of 𝑂𝐷
̅̅̅̅
1. 𝐶𝑂
_______________________________________
2. ___________________________________
Definition of midpoint
3. ___________________________________
_______________________________________
4. ∆𝐶𝑂𝐿 ≅ ∆𝐶𝐷𝐿
_______________________________________
Proof #4:
̅̅̅̅ bisect each other
Given: ̅̅̅̅
𝐴𝐸 and 𝐵𝐷
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶
Statements
Reasons
̅̅̅̅ bisect each other
1. ̅̅̅̅
𝐴𝐸 and 𝐵𝐷
_______________________________________
2. ___________________________________
Definition of segment bisectors
3. ___________________________________
_______________________________________
4. ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶
_______________________________________