Calculus Fall 2010 Lesson 01

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Lesson Plan #002

Class

: Geometry

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:

Date

: Monday September 10 th

, 2012

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?

_________________________________

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? _________________

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.

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

1

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

A) Point P

B) Line AB

C)

D)

Ray AB

Line Segment AB

2

Definition

: The

length or measure of a line segment

is the distance between its endpoints. AB represents the measure of

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?

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.

Question

:

AB

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

AB

A) The value of

x x

,

BC

x

6

, and

AC

24

. Find

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:

3

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