Exercise 23 Page 24

To determine whether the segments XY and ZW are congruent, let's consider the given points on the number line.

In order for segments to be congruent, they must have the same length. To find the length of a segment, we use the Ruler Postulate. This postulate states that the length of a segment is the absolute value of the difference between the points. Let's start by finding XY.

XY=|x-y|

SubstituteII

x= -7, y= - 3

XY=| -7-( - 3)|

SubNeg

a-(- b)=a+b

XY=|-7+3|

AddTerms

Add terms

XY=|-4|

AbsNeg

|-4|=4

XY=4

We know that XY has a length of 4. Now, let's find the length of ZW.

ZW=|z-w|

SubstituteII

z= 1, w= 5

ZW=| 1- 5|

SubTerm

Subtract term

ZW=|-4|

AbsNeg

|-4|=4

ZW=4

Since 4=4, XY equals ZW. Therefore, XY is congruent to ZW. XY= ZW ⇒ XY≅ZW