We are given a diagram that contains two triangles. We want to decide whether we have enough information to prove that the triangles are congruent using the AAS (Angle-Angle-Side) Congruence Theorem. If we decide that we do, we will write a proof. Otherwise, we will explain what information is missing. First, let's recall the AAS Congruence Theorem.
Angle-Angle-Side Congruence Theorem
If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
We can also visualize the AAS Congruence Theorem using a diagram.
Finally, we can focus on the given diagram.
Examining the diagram in the exercise, we see that the two triangles have two pairs of congruent angles and one pair of congruent non-included corresponding sides.
∠ E ≅ ∠ H, ∠ F ≅ ∠ J and FG≅JK
This is precisely what the AAS Congruence Theorem requires, so we are given enough information to claim congruence by the AAS Congruence Theorem. Let's write a two-column proof!
