Exercise 12 Page 404

Let's begin by plotting the points on a coordinate plane. Remember that the first value represents the x-coordinate and the second is the y-coordinate.

To determine if AB and CD are congruent, we should compare the length between A and B to the length between C and D. The length can be calculated by evaluating the absolute value of the difference between the x- or y-values, depending on if it is a horizontal or vertical line.

Let's start with calculating the length AB. Because it is a horizontal line, we take the absolute value of the difference between the x-values of A and B.

AB=|x_A-x_B|

SubstituteII

x_A= -8, x_B= 1

AB = | -8- 1|

SubTerm

Subtract term

AB = |-9|

AbsNeg

|-9|=9

AB = 9

The length of AB is 9. Now we should compare it with the length of CD. It is also a horizontal line, so we will calculate its length, the same way as AB.

CD=|x_C-x_D|

SubstituteII

x_C= 2, x_D= -2

CD = | -3- 5|

SubTerm

Subtract term

CD = |-8|

AbsNeg

|-8|=8

CD= 8

If two segments have the same lengths, they are congruent segments. The length AB is 9 and the length CD is 8. Therefore, they are not congruent.