Home › Coordinate geometry and transformations

Use the law of syllogism with rigid transformations

Chain two implications through their common statement

The law of syllogism says that if $P \Rightarrow Q$ and $Q \Rightarrow R$ , then $P \Rightarrow R$ . The middle statement $Q$ must mean the same thing in both premises.

Problem

Use the law of syllogism to complete the conclusion. Premise 1: If a polygon undergoes a rigid transformation, its image is congruent to the original. Premise 2: If an image is congruent to the original, their perimeters are equal. What follows?

Answer

If a polygon undergoes a rigid transformation, its image and the original polygon have equal perimeters.

The conclusion links the first condition to the final consequence; it does not require a third premise.

Step-by-step solution

1. Name the statements

Let $P$ mean that a polygon undergoes a rigid transformation, $Q$ mean that its image is congruent to the original, and $R$ mean that their perimeters are equal.

2. Chain the premises

The premises say $P \Rightarrow Q$ and $Q \Rightarrow R$ . By the law of syllogism, $P \Rightarrow R$ . In words: a rigid transformation leads to an image with the same perimeter as the original polygon.

Add to Chrome - solve your own

Screenshot any problem on your screen and get the steps. Chrome on a computer; free.