Exercise 15 Page 24

We are given a number line and we want to determine whether LN and MN are congruent. For two segments to be congruent, they must have the same length. This means that we want to find the distance between the points L and N and the distance between the points M and Q. Consider the given number line.

To find the distance between the points, we will first determine their coordinates using the Ruler Postulate.

Ruler Postulate

Every point on a line can be paired with a real number. This makes a one-to-one correspondence between the points on the line and the real numbers. The real number that corresponds to a point is called the coordinate of the point.

The distance between two points is the absolute value of the difference of their coordinates. Looking at the number line we can see that the coordinate of the point L is -8 and the coordinate of point N is 3.

LN=|l-n|

SubstituteII

l= -8, n= 3

LN=| -8- 3|

SubTerms

Subtract terms

LN=|-11|

AbsNeg

|-11|=11

LN=11

Now, let's find the length of MQ. Looking at the number line we can see that the coordinate of the point M is -3 and the coordinate of point Q is 12.

MQ=|m-q|

SubstituteII

m= -3, q= 12

MQ=| -3- 12|

SubTerms

Subtract terms

MQ=|-15|

AbsNeg

|-15|=15

MQ=15

The length of LN is 11 and the length of MQ is 15. Since 11≠15, LN does not equal MQ. Therefore, LN is not congruent to MQ. LN≠ MQ ⇒ LN≆MQ