Question

Decide weather there is enough information to prove the following triangles are congruent. Justify your answer for each pair of triangles.

Is DEF = DHG. Justify your answer below.

Answer 1

Yes there is enough information to find both triangles DEF and DHG are congruent.

Both the triangles are congruent by SAS theorem of congruence.

Explanation:

Lets have a look to both of the triangles.

And mention what are the given information in our question.

We have
`\triangle` DEF and
`\triangle` DHG.

Where

• FD
  `=` DG
• ED
  `=` DH

And we can see that
`\angle FDE = \angle HDG` (Vertically opposite angles).

So we have two sides equal and an angle between the two are equal.

Then we can say that through SAS property of congruence
`\triangle` DEF and
`\triangle` DHG are congruent
`\triangle` 's