Question

Match the reasons with the statements in the proof to prove DF = EF given that DEF is a triangle by definition and angles 3 and 4 are equal.

Given:
△DEF
∠3 = ∠4

Prove:
DF = EF

1. ∠3 = ∠4 Exterior Sides are in Opposite Rays
2. ∠1 and ∠3 are supplementary

∠2 and ∠4 are supplementary Two Angles Supplementary to Equal Angles are Equal to Each Other
3. ∠1 = ∠2 If the Two Angles of a Triangle are Equal, then the Sides Opposite those Angles are also Equal
4. DF = EF Given
pls hepl

Answer 1

1. ∠3 = ∠4 = Given

2. ∠1 and ∠3 are supplementary and ∠2 and ∠4 are supplementary = Exterior sides are in Opposite Rays

3. ∠1 = ∠2 = Two Angles Supplementary to Equal Angles are Equal to Each Other

4. DF = EF = If the Two Angles of a Triangle are Equal, then the Sides Opposite those Angles are also Equal

Explanation:

Answer 2

Proved that DF = FE.

Explanation:

See the given diagram attached.

In triangle Δ DEF, we have to prove DF = FE when ∠ 3 = ∠ 4.

The proof is like followings :

1. ∠3 = ∠4, Reason: Given

2. ∠1 and ∠3. Reason: They are supplementary.

∠2 and ∠4. Reason: They are supplementary.

3. ∠1 = ∠2. Reasons: Two Angles Supplementary to Equal Angles are Equal to Each Other.

4. DF = EF. Reason: Opposite sides of equal angles. (Answer)