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

Answer 1

Answer with explanation:

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. $\Bar{DE}=\Bar{E F}$

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