Question

Premises:

If two triangles are congruent, their corresponding angles are congruent.
△ABC and △QRS are not congruent.

Conclusion:
The corresponding angles of △ABC and △QRS are not congruent.



Which statement best describes this argument?

Responses

The argument is valid by the law of syllogism.
The argument is valid by the law of syllogism.

The argument is valid by the law of detachment.
The argument is valid by the law of detachment.

The argument is invalid because the conclusion does not follow the premises.
The argument is invalid because the conclusion does not follow the premises.

The argument is invalid because the premises are not true.

Answer 1

Answer: The argument is invalid because the conclusion does not follow the premises.

Further Explanation:

If triangles ABC and QRS aren't congruent, it doesn't mean the angles aren't congruent. It's certainly possible to have A = Q, B = R and C = S happen while the triangles aren't congruent.

Imagine the two triangles are similar to one another, but not congruent. This means one triangle is a smaller scaled copy of the other, or one is an enlarged copy. They have the same shape but different size.

So the premise "△ABC and △QRS are not congruent" does not automatically lead to the conclusion of "The corresponding angles of △ABC and △QRS are not congruent."