Exercise 18 Page 24

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|

SubstituteII

l= -8, p= 6

LP=| -8- 6|

SubTerm

Subtract term

LP=|-14|

AbsNeg

|-14|=14

LP=14

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

MQ=|m-q|

SubstituteII

m= -3, q= 12

MQ=| -3- 12|

SubTerm

Subtract term

MQ=|-15|

AbsNeg

|-15|=15

MQ=15

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