Exercise 13 Page 392

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 vertical line, we take the absolute value of the difference between the y-values of A and B.

AB=|y_A-y_B|

SubstituteII

y_A= 6, y_B= -1

AB = | 6-( -1)|

SubNeg

a-(- b)=a+b

AB = |7|

AbsPos

|7|=7

AB = 7

The length of AB is 7. Now we should compare it with the length of CD. To find the length of a horizontal segment, we should take the absolute value of the difference between C and D's x-values.

CD=|x_C-x_D|

SubstituteII

x_C= -4, x_D= 3

CD = | -4- 3|

SubTerm

Subtract term

CD = |-7|

AbsNeg

|-7|=7

CD= 7

If two segments have the same lengths, they are congruent segments. We can see that this is the case, both are equal 7. Therefore, they are congruent.