Question

1. use the law of syllogism to write a new conditional statement that follows from the pair of true statements. \if a triangle has three equal angles, then the triangle is an equiangular triangle.\ \if a triangle is an equiangular triangle, then the triangle has three equal sides\

Explanation:

Step1: Recall law of syllogism

The law of syllogism states that if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\). Let \(p\) be "a triangle has three equal angles", \(q\) be "a triangle is an equiangular triangle", and \(r\) be "the triangle has three equal sides".

Step2: Form new conditional

Combining the two given statements using the law of syllogism, we get: If a triangle has three equal angles, then the triangle has three equal sides.

Answer:

If a triangle has three equal angles, then the triangle has three equal sides.