Geometry Fall 2015 Lesson 002 (Lines, Line Segments, and Rays)



Lesson Plan #002

Class: Geometry Date: Monday September 21st, 2020

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:

Page 5 of this lesson plan

Do Now: What are some real-life examples of a ray.

PROCEDURE:

Write the Aim and Do Now

Get students working!

Take attendance

Go over the Do Now

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? Name 3 rays pictured below.

Definition: Opposite rays are two rays of the same line with a common endpoint and no other point in common.



In the picture at right, what are two opposite rays?

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?

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:

For which of the following figures could we determine a length?

A) Point P

B) Line AB

C) Ray AB

D) Line Segment AB

Assignment: Using a ruler, measure the length of [pic] in centimeters or inches.

Write your answer in the box at the right.

Definition: The length or measure of a line segment is the distance between its endpoints. AB represents the length of [pic].

Link:

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) [pic] |[pic] |

|Task:  To construct a line segment congruent to (line segment) [pic]. | |

Directions:

|1.  If a reference line does not already exist, draw a reference line with your straightedge upon which you will make |[pic] |

|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) [pic] are congruent.  Congruent means equal in length.

Explanation of construction:  The two line segments are the same length, therefore they are congruent. 

Assignment #1: Construct a line segment [pic]congruent to [pic]

Assignment #2: Construct a line segment[pic]

whose measure is twice AB.

Link:

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:

Question 1:

What is the length of AB, if line [pic] is the segment bisector and AO = 6 units?

Choices:

A. 13 units

B. 6 units

C. 12 units

D. 14 units

Exercise #1: In [pic], B is between A and C, [pic], [pic], and [pic]. Find

A) The value of [pic] B) BC

Example #1: Point M divides line segment AB, in the direction from A to B, in a ratio of 1 to 6. What value on the number line would indicate the location of point M?

Example #2: Point M divides line segment AB, in the direction from A to B, in a ratio of 3 to 8. What value on the number line would indicate the location of point M?

A) [pic] B) [pic] C) [pic] D) [pic] E) None of the other choices

A postulate is a statement whose truth is accepted without proof. The Segment Addition Postulate states that in [pic], if B is a point on [pic] between A and C, then [pic].

Group Work:

HW#2: Name Date Per.

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[pic]

[pic]

[pic]

[pic]

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