Question

pls solve this sum pls guys​

Answer 1

Answer:

Yes, ΔEHF is congruent to ΔGHF.

Yes, HF is the angle bisector of ∠EFG.

Given:

A ΔEFG where;

EF = GF

EH = GH

H is the midpoint of EG.

To prove:

ΔEHF ≅ ΔGHF

∠EFH = ∠GFH [Which implies that HF is the angle bisector of ∠EFG]

Proof:

In ΔEHF & ΔGHF;

EF = GF [Given]

EH = GH [Given]

FH = FH [Common side]

∴ Using SSS [Side-Side-Side] Congruency criterion, we can say that ΔEHF ≅ ΔGHF.

We also know that corresponding parts of congruent triangles are equal. [CPCT]

Therefore, ∠EFH = ∠GFH as they are corresponding parts of triangles ΔEHF and ΔGHF respectively.

We know that ∠EFH is equal to ∠GFH and that adding both the angles gives us ∠EFG. Therefore, the angle ∠EFG is divided into two equal parts (bisected), by the line HF.

Hence proved.