Exercise 24 Page 24

To determine whether the segments ZX and WY 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 ZX.

ZX=|z-x|

SubstituteII

z= 1, x= - 7

ZX=| 1-( - 7)|

SubNeg

a-(- b)=a+b

ZX=|1+7|

AddTerms

Add terms

ZX=|8|

AbsPos

|8|=8

ZX=8

We know that ZX has a length of 8. Now, let's find the length of WY.

WY=|w-y|

SubstituteII

w= 5, y= - 3

WY=| 5-( - 3)|

SubNeg

a-(- b)=a+b

WY=|5+3|

AddTerms

Add terms

WY=|8|

AbsPos

|8|=8

WY=8

Since 8=8, ZX equals WY. Therefore, ZX is congruent to WY. ZX= WY ⇒ ZX≅WY