Question

Tony examines two triangles. He wants to prove that if two pairs of corresponding sides are congruent and a pair of corresponding angles other than the included angles is congruent, then the two triangles are congruent. Which of the following best describes the problem with this approach?

a) It requires a multi-step proof.

b) It depends on theorems and postulates.

c) Geometric statements require geometric deduction.

d) A single counterexample will invalidate the proof.

Answer 1

The problem with Tony's approach is that it depends on theorems and postulates, and a single counterexample can invalidate the proof.

Step-by-step explanation:

The problem with Tony's approach is that it depends on theorems and postulates. In order to prove that two triangles are congruent, we need to use specific geometric statements and apply deductive reasoning based on postulates and theorems. Tony's approach assumes that two pairs of corresponding sides and a pair of corresponding angles other than the included angles being congruent are sufficient conditions for congruence, but this is not necessarily true. A single counterexample can invalidate this proof.