Exercise 25 Page 24

To determine whether the segments YZ and XW 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 YZ.

YZ=|y-z|

SubstituteII

y= - 3, z= 1

YZ=| -3- 1|

SubTerm

Subtract term

YZ=|- 4|

AbsNeg

|-4|=4

YZ= 4

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

XW=|x-w|

SubstituteII

x= - 7, w= 5

XW=| - 7- 5|

SubTerm

Subtract term

XW=|- 12|

AbsNeg

|-12|=12

XW=12

Since 4 ≠ 12, YZ does not equal XW. Therefore, YZ is not congruent to XW. YZ ≠ XW ⇒ YZ≆XW