Exercise 10 Page 16

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's a horizontal or vertical line.

Let's start with calculating the length AB. Because it's 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= 6, x_B= 1

AB = | 6- 1|

SubTerm

Subtract term

AB = |5|

AbsPos

|5|=5

AB = 5

The length of AB is 5. 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= 4

CD = | 2- 4|

SubTerm

Subtract term

CD = |-2|

AbsNeg

|-2|=2

CD= 2

If two segments have the same lengths, they are congruent segments. The length AB is 5 and the length CD is 2. Therefore, they are not congruent.