Question

Use the law of syllogism to form a conclusion from the given premises.

a) If 1 a polygon was translated to the right, then 2 a rigid transformation was performed.
b) If 1 an image is congruent to its pre-image, then 2 a rigid transformation was performed.

Answer 1

The law of syllogism is applied by linking the premises that both involve rigid transformations, leading to the conclusion that if a polygon is translated to the right, then its image is congruent to its pre-image.

Step-by-step explanation:

To use the law of syllogism to form a conclusion from the given premises, we need to identify a chain of reasoning where one conclusion leads to the next premise. The premises given are:

1. If a polygon was translated to the right, then a rigid transformation was performed.
2. If an image is congruent to its pre-image, then a rigid transformation was performed.

These premises can be reformulated using propositional logic as follows:

1. If P, then Q. (If a polygon is translated to the right, then a rigid transformation has occurred.)
2. If R, then Q. (If an image is congruent to its pre-image, then a rigid transformation has occurred.)

The law of syllogism allows us to combine these premises to draw a new conclusion. Since both premises conclude that a rigid transformation has occurred (Q), we can infer that:

If a polygon is translated to the right, then an image is congruent to its pre-image (If P, then R).

This conclusion is the product of valid deductive reasoning, according to the law of syllogism, because the occurrence of a rigid transformation links the initial action (translation to the right) with the result (congruence of image and pre-image).