Use a paragraph, flow chart, or two-column proof to prove the angle congruence. given: cxy ≅ bxy cax ≅ bax ac≅ ab prove: xcy ≅ xby

The Question is Incomplete with the Figure,So the complete Question with Diagram is below.  

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

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

312312

step-by-step explanation: