Question

Use a paragraph, flow chart, or two-column proof to prove the angle congruence. Given: CXY ≅ BXY CAX ≅ BAX AC≅ AB Prove: XCY ≅ XBY

Answer 1

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