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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

3. Measuring Segments

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Exercise 23 Page 24

What does it mean for segments to be congruent?

Segment Lengths: XY=4 and ZW=4
Congruent? Yes

Practice makes perfect

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|

x= -7, y= - 3

XY=| -7-( - 3)|

a-(- b)=a+b

XY=|-7+3|

Add terms

XY=|-4|

|-4|=4

XY=4

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

ZW=|z-w|

z= 1, w= 5

ZW=| 1- 5|

Subtract term

ZW=|-4|

|-4|=4

ZW=4

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

Subchapter links

Lesson Check p.23

Practice and Problem-Solving Exercises p.24-25

Standardized Test Prep p.26

Mixed Review p.26