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Lesson Plan #002
Class: Geometry
Date: Monday September 8th, 2014
Topic: Segments, rays, and distance
Aim: What are some definitions involving lines and line segments?
Objectives:
1) Students will be able to describe what is a line segment and a ray.
HW# 002:
Do Now: The intersection of two figures is the set of points that are in both figures.
What is the intersection of the two planes shown at right?
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PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Go over the Do Now
If we examine part of a line with endpoints, then what figure do we have?
_________________________
Definition: A line segment is a set of points consisting of two points on a line called endpoints and
all the points on the line between the endpoints.
How can we denote a line segment? _________________
Online Activity: http://www.mathsisfun.com/definitions/line-segment.html
Definition: A ray is part of a line that consists of a point on the line, called an endpoint, and all the points on one side of
the endpoint.
How can we name a ray?__________________________
Definition: Opposite rays are two rays of the same line with a common endpoint and no
other point in common.
http://www.mathopenref.com/oppositerays.html
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In the picture at right, what are two opposite rays?
For which of the following figures could we determine a length?
A) Point P
B) Line AB
C) Ray AB
D) Line Segment AB
Definition: The length or measure of a line segment is the distance between its endpoints. AB represents the measure of AB .
Link: http://www.mathopenref.com/congruentlines.html
Definition: Congruent segments are segments that have the same length.
How could we denote that line segments AB and CD are congruent?
How could we denote that line segments AB and CD have the same length?
Constructions
1) To construct a line segment congruent (equal in length) to a given line segment
Given: (Line segment)
Task: To construct a line segment congruent to (line segment)
.
Directions:
1. If a reference line does not already exist, draw a reference line with your straightedge upon
which you will make your construction. Place a starting point on the reference line.
2. Place the point of the compass on point A.
3. Stretch the compass so that the pencil is exactly on B.
4. Without changing the span of the compass, place the compass point on the starting point on the reference line and swing the
pencil so that it crosses the reference line. Label your copy.
Your copy and (line segment)
are congruent. Congruent means equal in length.
Explanation of construction: The two line segments are the same length, therefore they are congruent.
Assignment: Construct a line segment
A
CD congruent to AB
B
Assignment: Construct a line segment EF whose measure is twice AB
A
B
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Link: http://www.mathopenref.com/midpoint.html
Definition: The midpoint of a segment is the point of that line segment that divides the segment into two
congruent segments. If C is the midpoint of line segment AB, what statement of congruence can we make?
____________
What statement of equality can we make?
The bisector of a line segment is any line or subset of a line that intersects the segment at its midpoint.
Link: http://www.mathopenref.com/bisectorline.html
Question:
What is the length of AB, if line
l
is the segment bisector and AO = 6 units?
Choices:
A. 13 units
B. 6 units
C. 12 units
D. 14 units
Exercise: B is between A and C, with
A) The value of
AB  x , BC  x  6 , and AC  24 . Find
x
B) BC
The above exercise illustrates the Segment Addition Postulate. A postulate is a statement whose truth is accepted without proof.
The Segment Addition Postulate states that if B is between A and C, then AB  BC  AC .
Continue answering the following questions:
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On Your Own:
If Enough Time:
1)
2) Use the isosceles triangle to approximate the area under the curve.