Question

vanessa tried to prove that $\triangle klm \cong \triangle mnk$.
image of a quadrilateral with triangles inside, and a table with statements and reasons, followed by the question: what is the first error vanessa made in her proof? choose 1 answer:

• vanessa used an invalid reason to justify the congruence of a pair of sides or angles.
• vanessa only established some of the necessary conditions for a congruence criterion.
• vanessa established all necessary conditions, but then used an inappropriate congruence criterion.
• vanessa used a criterion that does not guarantee congruence.

Explanation:

To prove triangle congruence using SSS (Side - Side - Side), we need three pairs of corresponding sides to be congruent. Vanessa has only established two pairs of sides ($KL\cong MN$ and $LM\cong NK$) as congruent. The SSS criterion requires three pairs, so she only established some of the necessary conditions for the SSS congruence criterion. Option A is incorrect because the reasons for the first two statements are "Given", which is valid. Option C is incorrect as she didn't establish all necessary conditions for SSS. Option D is incorrect because SSS is a valid congruence criterion, but she didn't meet its requirements.

Answer:

B. Vanessa only established some of the necessary conditions for a congruence criterion.