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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 17 Page 24

What does it mean for segments to be congruent?

MN≅PQ

Practice makes perfect

To determine whether the segments MN and PQ 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 MN.

MN=|m-n|

m= -3, n= 3

MN=| -3- 3|

Subtract term

MN=|-6|

|-6|=6

MN=6

We know that MN has a length of 6. Now, let's find the length of PQ.

PQ=|p-q|

p= 6, q= 12

PQ=| 6- 12|

Subtract term

PQ=|-6|

|-6|=6

PQ=6

Since 6=6, MN equals PQ. Therefore, MN is congruent to PQ. MN= PQ ⇒ MN≅PQ

Subchapter links

Lesson Check p.23

Practice and Problem-Solving Exercises p.24-25

Standardized Test Prep p.26

Mixed Review p.26