Question

Which postulate or theorem proves that these two triangles are congruent?

ASA Congruence Postulate

SAS Congruence Postulate

AAS Congruence Theorem

HL Congruence Theorem

Answer 1

AAS congruence theorem.

We know that <H is congruent to <F and <GJH is congruent to <JGF.

We also know that JG is congruent to JG, which gives us a side and two angles, so AAS would prove them congruent.

Answer 2

ASA Congrence Postulate

Explanation:

Let us consider the Triangle FGJ and triangle GJH

1) angle GFJ =angle GHJ (given in the figure )

2) GJ=GJ (common side for both the triangles)

3)angle FGJ =angle GJH (alternate interior angles )

So, from the points (1),(2) and (3) we can say that both the triangle are congruent by ASA congruency .