Question

use the law of syllogism to form a conclusion from the given premises. premise 1: if a polygon was translated to the right, then its image is congruent to its pre - image. premise 2: if an image is congruent to its pre - image, then a rigid transformation was performed. select from the drop - down menus to correctly complete the conclusion. conclusion: if choose, then choose. choose: a rigid transformation was performed, an image is congruent to its pre - image, a polygon was translated to the right, a figure is a polygon

Explanation:

Step1: Identify the law of syllogism

The law of syllogism states that if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\).

Step2: Assign \(p\), \(q\), and \(r\)

Let \(p\) be "a polygon was translated to the right", \(q\) be "its image is congruent to its pre - image", and \(r\) be "a rigid transformation was performed".
Premise 1 is \(p
ightarrow q\) and Premise 2 is \(q
ightarrow r\).

Step3: Apply the law of syllogism

By the law of syllogism, since \(p
ightarrow q\) and \(q
ightarrow r\), we can conclude \(p
ightarrow r\). So if \(p\) (a polygon was translated to the right) then \(r\) (a rigid transformation was performed).

Answer:

If a polygon was translated to the right, then a rigid transformation was performed.