Question

choose the correct answer below.
a. he cannot assume they are the same length. the only information given in the diagram is that two pairs of sides of △abc and △bcd are congruent, which is not sufficient to prove △abc and △bcd congruent.
b. he cannot assume they are the same length. only one set of congruent angles and two sets of congruent sides are given for △abc and △bcd in the figure, and the angles are not between sides. ssa is not a criterion for congruence.
c. he is correct. △abc and △bcd are congruent by sss. ac and bd are congruent by cpctc.
d. he is correct. △abc and △bcd are congruent by sas. ac and bd are congruent by cpctc.

Explanation:

Step1: Analyze congruence criteria

Congruence of triangles requires specific criteria (SSS, SAS, ASA, AAS, HL). Here, only two pairs of sides are given.

Step2: Check SSA (Side - Side - Angle)

SSA is not a valid congruence criterion. Just having two sides and a non - included angle (which is the case if we assume something without proper proof) doesn't guarantee congruence.

Answer:

B. He cannot assume they are the same length. Only one set of congruent angles and two sets of congruent sides are given for \( \triangle ABC \) and \( \triangle BCD \) in the figure, and the angles are not between sides. SSA is not a criterion for congruence.