Question

Proof. Write a two-column proof. Given: ∠1 ≅∠4, ∠2 ≅∠3Prove: ∠AFC ≅∠EFC

Answer 1

Angle AFC is congruent to Angle EFC. is proved using Ange addition postulate

How to complete the proof

The two column proof is written as follows

Statement Reason

∠1 ≅ ∠4 given

∠2 ≅ ∠3 given

∠1 + ∠2 = ∠ AFC Ange addition postulate

∠3 + ∠4 = ∠ EFC Ange addition postulate

∠1 + ∠2 = ∠3 + ∠4 Substitution property of equality

∠ AFC ≅ ∠ EFC Definition of congruence

Answer 2

As all the angles are congruent we get that

`m\angle1+m\angle2=m\angle3+m\angle4`

and therefore

`\angle AFC\cong EFC`