Exercise 9 Page 56

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= 8, x_B= 3

AB = | 8- 3|

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. To find the length of a vertical segment, we should take the absolute value of the difference between C and D's y-values.

CD=|y_C-y_D|

SubstituteII

y_C= 1, y_D= -3

CD = | 1-( -3)|

SubNeg

a-(- b)=a+b

CD = |4|

AbsPos

|4|=4

CD= 4

If two segments have the same lengths they are congruent segments. The length of AB is 5 and the length of CD is 4. Therefore, they are not congruent.