Question

1. which rule explains why these triangles are congruent? sas aas asa sss these triangles cannot be proven congruent.

Explanation:

Step1: Recall congruence rules

Triangles congruence rules:

• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.

Step2: Analyze the given triangles

In \(\triangle GKJ\) and \(\triangle GHJ\):

• We have \(\angle K=\angle H\) (given as equal angles).
• \(GJ = GJ\) (common side, so one pair of sides is equal).
• \(\angle KGJ=\angle HGJ\) (given as equal angles).

Here, we have two angles (\(\angle K=\angle H\) and \(\angle KGJ=\angle HGJ\)) and a non - included side (\(GJ\)) that are equal.

Answer:

AAS