Question

analyzing triangle relationships
which congruency theorem can be used to prove that \\( \triangle ghl \cong \triangle khj \\)?
asa
aas
sss
sas

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So, \(\angle GHL=\angle KHJ\)

Step2: Analyze given information

We have one pair of equal angles (\(\angle G=\angle K\) as marked), one pair of equal sides (the sides with tick marks, \(GH = KH\)) and the pair of vertical angles (\(\angle GHL=\angle KHJ\))

Step3: Recall congruence theorems

ASA (Angle - Side - Angle) congruence theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. Here, \(\angle G=\angle K\), \(GH = KH\), \(\angle GHL=\angle KHJ\) (two angles and the included side)

Answer:

ASA