Answer:
B. ASA (Angle-Side-Angle).
Step-by-step explanation:
We have been given a diagram and we are asked to find the congruence theorem, which will prove that △GHL ≅ △KHJ.
Upon looking at our diagram we can see that side length GH of △GHL is equal to side length KH of △KHJ.
We are also given that [tex]m\angle HGL=m\angle HKJ[/tex].
We can see that [tex]\angle GHL[/tex] is vertical opposite angle of [tex]\angle KHJ[/tex] as they are formed by the intersection of line segments GK and JL. Therefore, [tex]m\angle GHL\cong m\angle KHJ[/tex], by vertical angles theorem.
We can see that both triangles have two congruent angles and one congruent included side, therefore, △GHL ≅ △KHJ by ASA congruence and option B is the correct choice.
