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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

3. Measuring Segments

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Exercise 18 Page 24

What does it mean for segments to be congruent?

LP≆MQ

Practice makes perfect

To determine whether the segments LP and MQ are congruent, let's consider the given 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 LP.

LP=|l-p|

l= -8, p= 6

LP=| -8- 6|

Subtract term

LP=|-14|

|-14|=14

LP=14

We know that LP has a length of 14. Now, let's find the length of MQ.

MQ=|m-q|

m= -3, q= 12

MQ=| -3- 12|

Subtract term

MQ=|-15|

|-15|=15

MQ=15

Since 14≠15, LP does not equal MQ. Therefore, LP is not congruent to MQ. LP≠ MQ ⇒ LP≆MQ

Subchapter links

Lesson Check p.23

Practice and Problem-Solving Exercises p.24-25

Standardized Test Prep p.26

Mixed Review p.26