section 7.2 : measuring segments · 2019. 10. 13. · homework – section 7.2 : measuring segments...
TRANSCRIPT
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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.
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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 .
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(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 .
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(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 ?
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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.
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11. Given that A is the midpoint of , find and .
12. Given that D is the midpoint of , , and , find and .