1-4 Angle Measure

What is a protractor and why is it used?

You measured line segments.

• Measure and classify angles.

• Identify and use congruent angles and the bisector of an angle.

Vocabulary

Ray part of a line. It has one endpoint and extends infinitely in one direction.

D O G

To name a ray, start with the endpoint followed by another point on the ray.

P O N M

Vocabulary

Opposite rays are two rays sharing a common end point.

VocabularyAngle is formed by two rays (that are not

collinear) with a common endpoint or vertex. The two rays are the sides of the angle.

R

S

T

vertex

side

side

An angle is named by using three different letters. The vertex letter is always in the middle. When there are no other angles around, the angle may be named by the letter at the vertex.

Vocabulary

An angle divides a plane into three distinctive parts:

On the angle

In the interior of the angle

In the exterior of the angleR

S

T

vertex

side

side

W

X

Name the angle in four ways.

A

B

C

1

Measuring Angles

Angles have different sizes and are usually measured in degrees.

Angles measure between 0° and 180°.

The measure of an angle is written

The size of of an angle is not the same thing as the angle itself.

80XYZm

Protractor

Using a Protractor to measure

Using a protractor to measure

More Vocabulary

A. Measure TYV and classify it as right, acute, or obtuse.

Answer: mTYV = 90, so TYV is a right angle.

Measure and Classify Angles

Measure and Classify Angles

Answer: 180 > mWYT > 90, so WYT is an obtuse angle.

Measure and Classify Angles

Example 3INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH HCI, mGBH = 2x + 5, and mHCI = 3x – 10.

Example 3

GBH HCI Given

mGBH = mHCI Definition of congruent angles

2x + 5 = 3x – 10 Substitution

2x + 15 = 3x Add 10 to each side.

15 = x Subtract 2x from each side.

Step 1 Solve for x.

Example 3

Step 2 Use the value of x to find the measure of either angle.

.

Answer: mGBH = 35, mHCI = 35

Construction: Copy an Angle1. Draw an angle to copy.

2. Draw a ray for your construction area.

3. Put the sharp tip of your compass on the vertex (point) of the angle to copy.

4. Draw an arc crossing both sides of the angle

5. Without changing the size of your compass, put the point on the end point of your ray. Make an arc.

6. Go back to the angle and put each point of your compass on the spot that the arc crosses the sides of the angle.

7. Without moving the size of the compass, put the pointed tip on the spot where the arc crosses the ray. Make a mark that crosses the arc.

8. Connect the endpoint and the curved “X” to finish your constructed angle.

You have constructed congruent angles!!

Copy an Angle

Construction: Bisect an Angle1. Draw an angle on your paper.

2. Put the point of your compass on the vertex and draw a large arc.

3. Without moving the compass, put the point on the bottom side where the arc crossed the side. Make a mark in the interior of the angle.

4. Turn the compass and put the point on the other side where the arc crosses the side. Make a mark in the interior of the angle crossing the other mark.

5. Draw a ray connecting the vertex and the “X”.

You have bisected an angle!!

Assignment 1-4

p. 41, 13-17 odd, 21-25 odd, 33, 35, 47, 49