Question

Your friend claims that two

isosceles triangles ΔABC and
ΔDEF are congruent if two
corresponding sides are
congruent. He explains that there
are only two different lengths of
sides, so if AB ≅ DE and BC ≅ EF,
then it must follow that CA ≅ FD.
Explain the error in his reasoning.
(3 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The error in your friend's reasoning lies in the fact that he assumes that the two triangles only have two different lengths of sides. In reality, there are multiple ways that isosceles triangles can be constructed with different side lengths. Just because two corresponding sides are congruent does not guarantee that all three sides are congruent. This means that it is not enough to only show that two pairs of sides are equal to prove that the two triangles are congruent. More information, such as an additional pair of corresponding sides or angles being equal, is required to prove the congruence of the triangles.