Section 7.2 : Measuring Segments

Learning Targets: G.CO.1, G.CPE.6

Important Terms and Definitions

Coordinate: Every point on a number line can be paired with a real number. A coordinate is the real number that corresponds to a point.

Distance: The distance between any two points on a number line is the absolute value of the difference of their coordinates. In the figure below, the distance between A and B would be written as .

Segment Addition Postulate: If points A, B, and C are collinear, and B is between A and C, then .

Congruent Segments: two segments with the same length

Symbol: We write: Note: When talking about numerical values (the actual lengths), we use an equal sign.

Midpoint of a Segment: A point that divides the segment into two congruent segments.

Segment Bisector: A point, segment, ray or line that intersects a segment at its midpoint.

Finding Distance

Example: Find the distance between G and K.

(ex 1) Find the following distances in the given figure.

a) Distance between G and H b) Distance between G and K c) Distance between H and P d) Distance between K and M e) Distance between G and P

Using Segment Addition Postulate

Example: In the figure at the right, if MR is 46, find MP and PR.

What else could we have done to find PR?

(ex 2) In the figure below, if and , find .

(ex 3) In the figure below, . What are and ?

Congruent Segments

(ex 4) Use the number line below to determine whether or not the pairs of segments are congruent.

a) and b) and

Midpoint of a Segment

Example: Given that M is the midpoint of , find RM, MT and RT.

Since .

(ex 5) Given that A is the midpoint of , find GA, AF and GF.

(ex 6) If C is the midpoint of , D is the midpoint of , E is the midpoint of , F is the midpoint of , G is the midpoint of , H is the midpoint of , and , what is ?

Homework – Section 7.2 : Measuring Segments

Find the distances in the given figure.

1. Distance between G and H 2. Distance between G and K 3. Distance between H and P 4. Distance between K and M 5. Distance between G and P

6. Using the number line below, find two possible coordinates for C such that .

7. In the figure below, . What are and ?

8. In the figure below, . What are and ?

9. What algebraic expression represents GK in the figure below? If , what are GH and JK?

10. A nurse assistant at St. Elizabeth Hospital must cut a 12-foot piece of tubing to connect two patients to an oxygen regulator. The length of one of the pieces must be twice the length of the other piece. Make a drawing and write a segment addition equation to model the tubing lengths. Then find the length of the shorter segment of tubing.

11. Given that A is the midpoint of , find and .

12. Given that D is the midpoint of , , and , find and .