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In today’s lesson, we’re going to explore another building block in geometry, line segments.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Section 1.2 Measuring and Constructing Segments 15 Using the Segment Addition Postulate The cities shown on the map lie approximately in a straight line. Find the distance. 1.3 Using Midpoint and Distance Formulas For use with Exploration 1.3. Into two congruent line segments. Then bisect ABand use the result to find the midpoint M.
Line segments are used throughout this course to define all the geometric shapes such as rectangles, squares, trapezoids, etc.
We’re going to learn how to measure, find midpoints, and calculate the distance of line segments, so let’s get started!
Line vs Line Segment
A line is a perfectly straight path whose length extends indefinitely and has no width. Every line contains infinitely many points and is represented by a straight line with two arrow heads.
On the other hand, a line segment has a finite length denoted by its endpoints. The line segment contains infinitely many points between the endpoints and also has zero width.
Since a line segment has finite length, it’s measurable. Therefore, we’ll be able to use a new postulate to help us determine its exact length.
Ruler Postulate
The ruler is a model for the number line and points can be matched one to one with real numbers. These are called coordinates. The distance between two points on a line is the positive difference between the coordinates (corresponding numbers are a line). See the video below for further information, along with an example.
Congruent Segments
What’s congruence, you may ask?
Well, congruence is a mathematical word that means two things are equal. As Math is Fun nicely points out, the word originates from Latin congruere which means “to agree”. So if two things are congruent, they “agree.”
Consequently, we are going to show that if two segments have the same measure (length) then they are congruent. In order to do this, we will need to use the Segment Addition Postulate.
Segment Addition Postulate
This postulate states that the sum, or total length, of a segment, is comprised of the addition of smaller segments.
Segment Addition Postulate Definition
Midpoint Of A Line Segment
To find the midpoint of the line segment you’ll need to use the midpoint formula. Klokki 1 1 3 download free.
Formula
Example
Distance Of A Line Segment
To find the distance of a line segment you’ll need to use the distance formula.
Formula
Example
How to Find the Distance of a Line Segment
Together we will look at how to determine lengths of segments using the ruler postulate, understand what the midpoint of a segment and a segment bisector are, use the Segment Addition Postulate to calculate the lengths of segments, and use the coordinate plane and the formulas for distance and midpoint to determine the congruence of given segments.
Line Segments – Lesson & Examples (Video)
58 min
- Introduction to line segments and their measures
- 00:00:27 – What is a Postulate? Using the Ruler Postulate (Examples #1-4)
- 00:07:16 – What are congruent segments and segment bisectors? (Example #5-13)
- Exclusive Content for Member’s Only
- 00:18:13 – The segment addition postulate explained (Examples #14-19)
- 00:26:28 – Use the segment addition postulate to find the length of each segment (Examples #20-21)
- 00:38:34 – Use the midpoint formula to find missing coordinates in a coordinate plane (Examples #22-25)
- 00:49:55 – Understanding the distance formula and using it to prove congruent segments
- Practice Problems with Step-by-Step Solutions
- Chapter Tests with Video Solutions
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Section 1.2 Measuring Segments
G.4.5 Prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula,
and various forms of equations of lines and circles.
and various forms of equations of lines and circles.
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Line Segment Distance Calculator
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Line Segment
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