Question

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

Explanation:

Step1: Recall Congruence Rules

• 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.
• 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.
• 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.

Step2: Analyze the Given Triangles

In the given triangles \(\triangle BGF\) and \(\triangle BCF\), we have two pairs of angles (\(\angle G=\angle C\) and \(\angle BFG = \angle BFC\)) and a non - included side (the side \(BF\) is common to both triangles).

Answer:

AAS