Question

explain whether there is enough information given in the figure to prove that the triangles are congruent using sss or sas. select choice ∠glh and ∠jlk are select choice angles, so they select choice congruent. therefore, △glh is select choice to △jlk by the select choice congruence postulate.

Explanation:

Step1: Identify Vertical Angles

∠GLH and ∠JLK are vertical angles (formed by intersecting lines), so they are congruent.

Step2: Check Side Markings

From the figure, we see that two pairs of sides are marked as equal (indicating congruent segments). Let's denote the sides: \( GL = JL \) (marked), \( HL = KL \) (marked), and we know \( \angle GLH \cong \angle JLK \) (vertical angles).

Step3: Apply SAS Congruence

By the SAS (Side - Angle - Side) congruence postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. Here, in \( \triangle GLH \) and \( \triangle JLK \), \( GL = JL \), \( HL = KL \), and \( \angle GLH=\angle JLK \) (included angle), so \( \triangle GLH \cong \triangle JLK \) by SAS.

Answer:

1. ∠GLH and ∠JLK are vertical angles, so they are congruent. Therefore, \( \triangle GLH \) is congruent to \( \triangle JLK \) by the SAS Congruence Postulate.