Question

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

Explanation:

Step1: Identify congruent sides

In triangles \( \triangle HCG \) and \( \triangle FCG \), we see that \( HG = FG \) (marked with two ticks), \( HC = FC \) (marked with one tick), and \( CG \) is a common side, so \( CG = CG \).

Step2: Apply congruence rule

The SSS (Side - Side - Side) congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent. Since we have three pairs of equal sides (\( HG = FG \), \( HC = FC \), \( CG = CG \)), the SSS rule applies.

Answer:

SSS (along with the option description: The rule that explains why these triangles are congruent is SSS, so the answer is the option labeled "SSS")