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\ if ______________________________________, then ______________________________________

Explanation:

Step1: Recall law of syllogism

The law of syllogism states that if we have two conditionals: "If $P$, then $Q$" and "If $Q$, then $R$", we can conclude "If $P$, then $R$".

Step2: Identify P, Q, R

Let $P$ = "a triangle has three equal angles", $Q$ = "the triangle is an equiangular triangle", $R$ = "the triangle has three equal sides".

Step3: Apply syllogism

Combine the two statements using the structure of the law of syllogism.

Answer:

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