1. Other Methods of Proving Triangles Congruent
Section 4-5:
Other Methods of Proving Triangles Congruent

2. Definition of right ∆’s
1. Supply the missing statements and reasons. Given: 𝑋𝑌 ⊥ 𝐴𝐵 ; 𝑋𝐴 ≅ 𝑋𝐵 Prove: ∠1 ≅ ∠2 STATEMENT REASONS 1. 𝑋𝑌 ⊥ 𝐴𝐵 1. ______________________ 2. ∠3 and ∠4 are right angles 2. ______________________ 3. ∆AYX and ∆BYX are right ∆’s 3. _______________________ 4. 𝑋𝑌 ≅ 𝑋𝑌 4. _______________________ 5. _______ ≅ ________ 5. Given 6. ∆AYX ≅ ___________ 6. ________________________ 7. ________________________ 7. ________________________
Given
Definition of ⊥ lines
Definition of right ∆’s
Reflexive Prop
𝑋𝐴 𝑋𝐵
∆BYX
HL Theorem
∠1 ≅ ∠2
CPCTC

3. 2. Given: 𝑌𝐴 ⊥ 𝐴𝐶 ; 𝑍𝐶 ⊥ 𝐴𝐶 ; B is the midpoint of 𝐴𝐶 ; 𝑌𝐴 ≅ 𝑍𝐶 Prove: ∠ABY ≅ ∠CBZ STATEMENTS REASON
𝑌𝐴 ⊥ 𝐴𝐶 ; 𝑍𝐶 ⊥ 𝐴𝐶
Given
m∠A = 90°; m∠C = 90°
Def. of ⊥ lines
∠A ≅ ∠C
Def. of ≅ angles
B is the midpoint of 𝐴𝐶
Given
𝐴𝐵 ≅ 𝐶𝐵
Def. of midpoint
𝑌𝐴 ≅ 𝑍𝐶
Given
∆𝐴𝐵𝑌 ≅ ∆CBZ
SAS Post.
∠ABY ≅ ∠CBZ
CPCTC

4. 3. Given: ∠V ≅ ∠W; 𝐶𝐷 bisects ∠VCW
Prove: 𝐷𝑉 ≅ 𝐷𝑊
Statements Reasons
1. ∠V ≅ ∠W; 𝐶𝐷 bisects ∠VCW
1. Given
2. ∠VCD ≅ ∠WCD
2. Def. of ∠ bisector
3. 𝐶𝐷 ≅ 𝐶𝐷
3. Reflexive Prop
4. ∆VCD ≅ ∆WCD
4. AAS Theorem
5. 𝐷𝑉 ≅ 𝐷𝑊
5. CPCTC

5. 4. Given: 𝐸𝐹 ⊥ 𝐸𝐺 ; 𝐻𝐺 ⊥ 𝐸𝐺 ; 𝐸𝐻 ≅ 𝐺𝐹
Prove: ∠H ≅ ∠F
Statements Reasons
1. 𝐸𝐹 ⊥ 𝐸𝐺 ; 𝐻𝐺 ⊥ 𝐸𝐺
1. Given
2. m∠FEG = 90°; m∠HGE = 90°
2. Def. of ⊥ lines
3. ∆EFG and ∆GHE are right ∆’s
3. Def. of right ∆’s
4. 𝐸𝐻 ≅ 𝐺𝐹
4. Given
5. 𝐸𝐺 ≅ 𝐸𝐺
5. Reflexive Prop
6. ∆EFG ≅ ∆GHE
6. HL Theorem
7. ∠H ≅ ∠F
7. CPCTC

6. HOMEWORK: page 142 #1-13 all (CE)