Question

which rule explains why these triangles are congruent?
j
k
g
f
m
h
asa
aas
sss
sas
these triangles cannot be
proven congruent.

Explanation:

To determine the congruence rule, we analyze the marked parts of the triangles. In triangle \( JKM \) and \( FGH \), we have two sides marked as equal (the double and single tick marks) and the included angle (the red - marked angle) between those sides. The SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Let's check the other options:

• ASA (Angle - Side - Angle) requires two angles and the included side to be equal. Here, we don't have two angles and the included side marked.
• AAS (Angle - Angle - Side) requires two angles and a non - included side to be equal. This is not the case here.
• SSS (Side - Side - Side) requires all three sides to be equal. We only have two sides marked as equal.

So, the triangles satisfy the SAS congruence rule.

Answer:

D. SAS (assuming the options are labeled as A. ASA, B. AAS, C. SSS, D. SAS, E. These triangles cannot be proven congruent. But based on the given options in the problem, if we consider the last option as E and SAS as D, the correct answer is D. SAS. However, if the options are presented as in the problem with the last option being "These triangles cannot be proven congruent", the correct option is the one labeled SAS among the given options. If we assume the options are ordered as ASA, AAS, SSS, SAS, "These triangles cannot be proven congruent", then the answer is the fourth option: SAS)