Question

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

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So, \(\angle HBG=\angle FBC\)

Step2: Analyze side - angle - side (SAS)

From the figure, \(HB = FB\), \(\angle HBG=\angle FBC\), \(BG = BC\). By the SAS (Side - Angle - Side) congruence rule, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Answer:

SAS