SAS Congruence Theorem requires that two sides and the included angle of two triangles are congruent.
There is enough information. Proof: See solution.
Practice makes perfect
According to the SAS Congruence Theorem, if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
What do we know about our triangles?
From the diagram, we see that ∠ GHF and ∠ KHJ are vertical angles. According to the Vertical Angles Congruence Theorem, vertical angles are congruent. Let's add this information to the diagram.
Can we use SAS?
Since two sides and the included angle of △ GHF are congruent with two sides and the included angle of △ KHJ, we can prove congruence by the SAS Congruence Theorem.
Two-column proof
Let's show this as a two-column proof.
Statement
Reason
1.
FH ≅ JH, GH ≅ KH
1.
Given
2.
∠ FHG and ∠ JHK are vertical angles
2.
Definition of vertical angles as seen in the diagram
