3 Geometry Angles

Tennessee Adult Education

GeometryLesson 3

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

What is Geometry?

•It is the branch of mathematics that deals with lines, points, curves, angles, surfaces, and solids.

Term Definition

The following key terms are important to know when discussing angles.

(•)

Point

Line

Line Segment

Ray

A specific location on an object or a specific position in space.

A connected set of points that extends without end in two directions.

A piece of a line, like a jump rope.

Part of a line that extends indefinitely in one direction.

Term Definition

Parallel Lines Lines that are always the same distance They will never intersect.

Perpendicular Lines

Lines that form a right angle when they intersect

Intersecting Lines Lines that cross, or that will cross. The point at which they cross is called the vertex.

Transversal Lines Lines that intersect a set of parallel lines.

What are angles?

•An angle measures the amount of a turn.•As the Angle Increases, the Name Changes.

Pictures from clipart

Mr. Smiles fell at an angle of 90⁰. He fell at a right angle.

Type of Angle Description

Acute An angle less than 90⁰

Right An angle that is exactly 90⁰

Obtuse An angle that is greater than 90⁰

Straight An angle that is exactly 180⁰

Reflex An angle that is greater than 180⁰

Find the Angles!

Walnut St. Bridge, Chattanooga

Parallel Lines

Review!

Right Angle

Obtuse Angle

Straight Angle

Perpendicular Lines

Parts of an AngleR

ay

Ray

·angle

Vertex

•The two straight sides are called rays.

• The point at which the two rays meet is called the vertex.

•The angle is the amount of a turn between each ray.

Naming Angles•There are two main ways to name angles:

1) Name an angle by the vertex.

For example: B is the point at which both rays intersect.

2) Name an angle by all three letters.

For example: A B C or C B A

HINT: The vertex is always the middle letter

A

B

C

Guided practice

•Directions: Name and classify the following angles. (Provide 3 ways to name each angle.) 1. 2.

3.4.

A

B C

C

E

F

G HKJ

I

DReflex Angle B ABC CBA

Acute Angle D CDE EDC

Obtuse Angle G FGH HGF

Right Angle J IJK KJI

Supplementary AnglesThe two angles below (140⁰ + 40⁰) are supplementary angles, because their measurements add up to 180⁰.

NOTICE: When the two angles are put together, they form a straight line.

Supplementary Angles

Supplementary cont.

But, the angles don't have to be together.These two are supplementary because:

60° + 120° = 180°

Complementary Angles

•The two angles at the right (40° + 50°) are Complementary Angles, because they add up to 90°.

•NOTICE: When the two angles are placed together, they form a corner.

Complementary cont.•But, the angles don't have to be together.•These two are complementary because their measurements add up to 90⁰.•

• 27° + 63° = 90°

Complementary Angles

Complementary vs Supplementary

How can you remember which is which? Easy! Think:

• "C" of Complementary stands for "Corner" (a Right Angle), and

• "S" of Supplementary stands for "Straight" (180 degrees is a straight line)

Find the missing angle using complementary or supplementary angles.

80


155


30


47

A

B

C

D

EF

<AFB and <BFC are complementary angles. If m<AFB = 50 ⁰, which expression could be used to find the measure of <BFC?

1. 180⁰ - 50 ⁰ 2. 90 ⁰ + 50 ⁰ 3. 180 / 50 ⁰ 4. 90 ⁰ (50 ⁰ )

Guided Practice1. The train crosses Sesame Street and Big Bird Avenue at

an angle of 60⁰. What is the measure of the supplementary angle?

Sesame St.

Big Bird Ave.HINT: a line equals 180⁰. 180 - 60 = 120⁰ ⁰ ⁰

2. Jo Jo is building a fence. In order to make it stronger, she will need to use a brace from one side to the ground. If the brace makes a 45⁰ angle with the fence what is the measure of the supplementary angle?

A transversal line is a line that cuts through a set of parallel lines.

As the transversal cuts through, it forms both Corresponding and Vertical Angles

Angles Formed by A Transversal

Transversal line

AB CD

Corresponding angles have equal measurements, and vertical angles have equal measurements.

This reads as Line AB is parallel to Line CD.

Corresponding Angles

The angles that occupy the same relative position at each intersection.

Therefore, the angles will have the same measurement.

2 & 6

The following angles are corresponding angles.

3 & 7

8&4

1 & 5

Example: If 3 is 130 , ⁰then 7 is also 130 . ⁰

Vertical Angles

E

BA

C D

F

2 1

3 4

56

7 8

Vertical angles are angles that are opposite from each other.

For example: 2 & 4 are vertical, because they are diagonal from each other.

Therefore, if 2 equals 50⁰, then 4 is also 50⁰.

Guided Practice

E

BA

C D

F

Directions: Fill in the missing angles if angle 1 equals 75⁰

2

6

Identify the vertical angles.

1. ________________

2. ________________

3. ________________

4. ________________

Identify the corresponding angles.

1. _________________

2. _________________

3. _________________

4. _________________

43

1

7 8

5

1

3

51

32

4

7

85

6 7

84

62

If the lines are parallel and m<2 is 45⁰ in the figure above, what is the measure of <3?

1. 30 ⁰ 2. 45 ⁰ 3. 90 ⁰ 4. 135 ⁰ 5. 180 ⁰

1

5 6

2 3 4

7 8

Vertical Angles vs. Corresponding

*Vertical angles are always equal. However, you can not assume you have corresponding angles unless dealing with a transversal.

Triangles

A triangle has three sides and three angles

The three angles always add up to 180°

a

b c

a + b + c = 180⁰

Why do I need to know about triangles?

The GED Test will ask testers to identify missing angles. In order to answer those questions, a person must have an understanding of triangles and their characteristics.

Equilateral, Isosceles and Scalene

There are three special names given to triangles that tell how many sides are equal.

Equilateral Triangle Three equal sides

Three equal angles, always 60°

Isosceles Triangle Two equal sides

Two equal angles

Scalene Triangle No equal sides

No equal angles

70

55

Find the missing angle measurement.

5050


6085


3 Geometry Angles

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