Question

△DEF

DF = EF

Prove:
∠3 = ∠4





Which of the following statements would be the reason in line 4 of the proof?

Answer 1

Given:

In Δ DEF, ∠3=∠4.

To prove:→ DE=E F

Proof:

1. ∠3=∠4------[Given]

2. →∠1 and ∠ 3 are Supplementary to each other.

(a)⇒∠1 + ∠ 3=180°

→∠2 and ∠ 4 are also Supplementary to each other.

(b)⇒∠2 + ∠ 4=180°

--------------------[Exterior sides in opposite rays]

3. From 1 , a and b

⇒∠ 1 = ∠ 2-------[Two Angles Supplementary to equal Angles are equal to each other]

4.

If two angles of a Triangle are equal , then side opposite to these angles are equal.

Answer 2

Two ∠'s supplementary to equal ∠'s are =

Explanation:

DF=EF means that the triangle is isosceles.

This means that the base angles are equal to each other.

Because the base angles are equal to each other, their supplementary must also be equal.