Question

Given: ∠GHD and ∠EDH are right; GH ≅ ED Which relationship in the diagram is true?

△GHD ≅ △EDH by SAS
△GHF ≅ △EDF by SSS
△FDH ≅ △FDE by ASA
△HFD ≅ △HFG by SSS

Answer 1

△GHD ≅ △EDH by SAS , got it right

Answer 2

△GHD ≅ △EDH by SAS

Explanation:

There are 3 types of congruences they are side angle side, side side side,

Angle side side.

We find that in the picture given above triangles GHF and EDF are having the following properties:

GH= ED(given)

angle GFH = angle EFD(vertically opposite angles)

But these two are sufficient to prove that the two triangles are congruent.

ii)

Triangles HFD and HFG

These two triangles have only HF = HF Hence cannot say congruent

iii) Consider triangles GHD and EDH

HD = HD (reflexive)

GH=ED(given)

Angle G = angle D (right angles)

Hence by SAS the two are congruent.