Lesson 1.1 (And Introduction to Measuring Angles)

Lesson 1.1

(And Introduction to Measuring Angles)

Objective:

Recognize points, lines, line segments, rays, angles, and triangles, and measure

segments, angles, and classify angles

Points:

Represented by capital letters (Draw 3 points and label them)

Lines:

Lines are made up of points and are straight. Arrows are drawn on the ends to show that the lines extend

infinitely far in both directions.

Basic Definitions

More on Lines:

Lines can be named based on any two points.

Let’s take a look at an example:

Name the line in 3 different ways.

Basic Definitions

A

Bl

Number Line:

A number line is formed when a numerical value is assigned to each point on a line.

Example:

Draw a number line from -2 to 3 using one tick mark per integer.

Basic Definitions

Line Segment:

Like lines, segments are made up of points and are straight, however, segments have a definite

beginning and end.

Line Segments are named by their endpoints.

Examples:

Name the following line segments

Basic Definitions

S

RX

P

Q

Rays:

Like lines and segments, rays are made up of points and are straight.

A ray differs from a line or segment in that it begins at an endpoint and extends infinitely far in only one

direction.

Examples:

Basic Definitions

D

C

K J

L

M

P

Note:

It is important to keep in mind that when we name a ray, we name the endpoint first! This makes it clear as to where the ray begins.

Name the following rays:

D

C

K J

L

M

P

Angles:

Two rays that have the same endpoint form an angle.

Def. An Angle is made up of two rays with a common endpoint. This point is called the vertex of the angle. The rays are called sides of the angle.

Examples:

Basic Definitions

C2A

P

H

1

B

2S

T

Naming Angles When naming an angle with 3 letters you must name the vertex in the middle! Every time…no exceptions!

Examples:

Name the following angles

C2A

P

H

1

B

2S

T

A triangle has three segments as its sides and three angles at each of its

vertices.

How could you name this triangle?

Triangles

B

A

C

Unions and Intersections are a way to help us see where certain pieces of an object overlap, and what they form when

pieced together.

In terms of a triangle:

The triangle is the union (U) of three segments:

The intersection (∩) of any two sides is a vertex of the triangle:

Unions and Intersections

ABC AB BC AC

AB BC B

B

A

C

a.

b.

c.

Example #1

______AC DE ���������������������������������������� ���

______AC BC ������������������������������������������

______BA BD ����������������������������

C

A

B

D m

E

Draw a diagram in which the intersection of with is segment

Example #2

AB��������������

CA��������������

AC

Segments can be measured using tools such as rulers or meter sticks, and often, segments found on

number lines can be measured by subtracting the ending and starting value.

Example:

Measuring Segments

P Q

Angles are measured using Protractors, and in this course we will be measuring angles in degrees.

The measure (or size) of an angle is the amount of turning you would do if you were at the vertex,

looking along one side, and then turned to look along the other side. (A surveyor’s transit works in a similar

way!)

Measuring Angles

Angles can be classified into four groups:

Classifying Angles by Size

Name Acute Angles Obtuse Angles Right Angles Straight Angles

Definition An angle whose measure is

greater than 0 and less than 90°

0< x < 90°

An angle whose measure is

greater than 90° and less than

180°

90°<x<180°

An angle whose

measure is 90°

An angle whose

measure is 180°

Picture

Lesson 1.1 Worksheet

Homework