Measuring and Constructing Segments

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Measuring and Constructing Segments
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
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Are you ready? Simplify. 1. 7 (3) 2. 1
(13) 3. 7 1 Solve each equation. 4. 2x 3
9x 11 5. 3x 4x 5 6. How many numbers
are there between and ?
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Objectives
TSW use length and midpoint of a segment. TSW
construct midpoints and congruent segments.
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When would I ever use this? You can measure a
segment to calculate the distance between two
locations. Maps of a race are used to show the
distance between stations on the course.
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Vocabulary
coordinate midpoint distance bisect length seg
ment bisector construction between congruent
segments
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A ruler can be used to measure the distance
between two points. A coordinate is a point
corresponds to one and only one number on a
ruler. The following postulate summarizes this
concept.
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Example 1 Finding the Length of a Segment
Find each length.
A. BC
B. AC
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Example 2
Find each length.
b. XZ
a. XY
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You can make a sketch or measure and draw a
segment. These may not be exact. A construction
is a way of creating a figure that is precise.
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• Constructing a Congruent Segment
• You will need a ruler and a compass.

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In order for you to say that a point B is between
two points A and C, all three points must lie on
the same line, and AB BC AC.
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Example 3 Using the Segment Addition Postulate
G is between F and H, FG 6, and FH 11. Find
GH.
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Example 3B Using the Segment Addition Postulate
M is between N and O. Find NO.
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Example 3c
Y is between X and Z, XZ 3, and XY .
Find YZ.
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Example 3d
E is between D and F. Find DF.
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Example 4 Recreation Application
The map shows the route for a race. You are 365m
from drink station R and 2km from drink station
S. The first-aid station is located at the
midpoint of the two drink stations. How far are
you from the first-aid station? What is the
distance to a drink station located at the
midpoint between your current location and the
first aid station?
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• B is the midpoint of AC , AB 5x, and BC 3x
  4. Find AB, BC and AC.

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Example 5 Using Midpoints to Find Lengths
D
E
F
4x 6
7x 9
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• A segment bisector is any ray, segment, or line
  that intersects a segment at its midpoint. It
  divides the segment into two equal parts at its
  midpoint.
• Lets construct one now.

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Lesson Quiz Part I
1. M is between N and O. MO 15, and MN 7.6.
Find NO.
3. Sketch, draw, and construct a segment
congruent to CD.
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Lesson Quiz Part II
4. LH bisects GK at M. GM 2x 6, and GK
24. Find x.
5. Tell whether the statement below is sometimes,
always, or never true. Support your answer with
a sketch. If M is the midpoint of KL, then M, K,
and L are collinear.
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Lesson Quiz Part I
1. M is between N and O. MO 15, and MN 7.6.
Find NO.
22.6
25, 25, 50
3. Sketch, draw, and construct a segment
congruent to CD.
Check students' constructions
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Lesson Quiz Part II
4. LH bisects GK at M. GM 2x 6, and GK
24. Find x.
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5. Tell whether the statement below is sometimes,
always, or never true. Support your answer with
a sketch. If M is the midpoint of KL, then M, K,
and L are collinear.
Always