Question

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

Explanation:

1. Identify the two triangles: $\triangle FCB$ and $\triangle FGB$.
2. List the given congruent parts:

• $BC = BG$ (marked with a single tick)
• $\angle C = \angle G$ (marked as right angles)
• $FB = FB$ (common side to both triangles)

1. Match to congruence rules: This is two sides and a non-included angle (the right angle is not between the side pair $BC/BG$ and the common side $FB$ for both triangles). None of the valid congruence rules (SAS, ASA, AAS, SSS) apply here, as SSA (side-side-angle) is not a valid triangle congruence criterion.

Answer:

These triangles cannot be proven congruent.