Question

Given the information below, write a proof that will allow you to state that ∠G ≅ ∠M.

Given: △FGH and △LMN with ∠F ≅ ∠L, (a vinculum is placed over all these letters) FG ≅ LM and FH ≅ LN.


Prove: ∠G ≅ ∠M

Your response should be in the form of a proof giving both the necessary statements and the reasons that justify them.

Answer 1

Given: △FGH and △LMN with FG≅LM, ∠F≅∠L, and FH≅LN.

To Prove ∠G≅∠M.

Reasons:

FG≅LM Given

FH≅LN Given

∠F≅∠L Given

△FGH≅△LMN (SAS Congruence Theorem)

∠G and ∠M are corresponding angles of △FGH≅△LMN

Therefore, ∠G≅∠M. Henced Proved.

Note:

The SAS congruence theorem can be used to prove that two triangles are congruent if we know that two sides and the included angle of one triangle are equal to the corresponding sides and included angle of the other.