Which conclusion can be drawn based on the true statements shown?If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.
Answer
A
Based on the law of syllogism, if all the angles in a triangle are congruent, then the triangle is equilateral.
B
Based on the law of detachment, if all the angles in a triangle are congruent, then the triangle is equilateral.
C
Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.
D
Based on the law of detachment, if a triangle is equilateral, then all the angles are congruent.
Explanation
Let P mean “the triangle is equilateral,” Q mean “all its sides are congruent,” and R mean “all its angles are congruent.” The statements give P → Q and Q → R, so the law of syllogism gives P → R. Therefore, if a triangle is equilateral, all its angles are congruent; this is choice C.
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