The Question is Incomplete with the Figure,So the complete Question with Diagram is below.
Answer:
The Proof is given Below.
Step-by-step explanation:
Given:
∠CXY ≅ ∠BXY
∠CAX ≅ ∠BAX
AC≅ AB
To Prove:
∠XCY ≅ ∠XBY
Proof:
In Δ AXC and Δ AXB
STATEMENT REASONS
1. AC ≅ AB 1. Given
2. ∠CAX ≅ ∠BAX 2. Given
3. AX ≅ AX 3. Reflexive Property
4. ΔAXC ≅ ΔAXB 4. Side-Angle-Side congruence test
5. ∴ CX ≅ BX 5.corresponding parts of congruent triangles........( 1 )
Now ,
In Δ XYC and Δ XYB
STATEMENT REASONS
1. CX ≅ BX 1. Proved above from ( 1 )
2. ∠CXY ≅ ∠BXY 2. Given
3. XY ≅ XY 3. Reflexive Property
4. ΔAXC ≅ ΔAXB 4. Side-Angle-Side congruence test
5. ∴ ∠XCY ≅ ∠XBY 5. Corresponding parts of congruent triangles...........Proved
