Question

Given: start overline, A, G, end overline, \cong, start overline, E, B, end overline, comma

AG
≅
EB
, angle, A, \cong, angle, B∠A≅∠B and start overline, C, D, end overline, \cong, start overline, C, F, end overline, .
CD
≅
CF
.

Prove: start overline, G, H, end overline, \cong, start overline, E, H, end overline
GH
≅
EH
.

Answer 1

We have proved that side GH is congruent to side EH i.e; GH ≅ EH.

To prove that GH ≅ EH , we can use the ASA (Angle-Side-Angle) criterion.

Given:

AG ≅ EB (Corresponding sides of congruent triangles)

∠A≅∠B (Corresponding angles of congruent triangles)

CD≅ CF (Corresponding sides of congruent triangles)

Now, we want to prove GH ≅ EH .

Here's the proof:

△AGH≅△EBH (By ASA):

∠AGH≅∠EBH (Common side GH and EH )

AG ≅ EB (Given)

∠A≅∠B (Given)

By CPCTC (Corresponding Parts of Congruent Triangles are Congruent):

This implies GH ≅ EH .

Therefore, GH ≅ EH is proved.

Question