3-1 Lines and Angles Geometry

1 / 38

# 3-1 Lines and Angles Geometry - PowerPoint PPT Presentation

3-1 Lines and Angles Geometry. Mrs. O’Neill. LINES AND ANGLES. Warm Up. The soccer team scored 3 goals in each of their first two games, 7 goals in the next game, and 2 goals in each of the last four games. What was the average (mean) number of goals the team scored per game?. 2). Warm Up.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about '3-1 Lines and Angles Geometry' - melvina-hartnett

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 3-1 Lines and AnglesGeometry

Mrs. O’Neill

Warm Up

The soccer team scored 3 goals in each of their first two games, 7 goals in the next game, and 2 goals in each of the last four games. What was the average (mean) number of goals the team scored per game?

2)

Warm Up

Solve the equation:

=

-20

=

-0.8

=

9

=

=

-1

MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Essential Questions

How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?

B

A

D

l

C

m

PARALLEL LINES

Lines that do not intersect

• Notation:l || mAB|| CD

Examples of Parallel Lines

• Opposite sides of windows, desks, etc.
• Parking spaces in parking lots
• Parallel Parking
• Streets in a city block

m

n

PERPENDICULAR LINES

Lines that intersect to form a right angle

• Notation:m n
• Key Fact: 4 right angles are formed.
any angle less than 90º

Acute Angle –

a 90º angle

Right Angle –

angles that add up to 90º

Complementary Angles –

angles that add up to 180º

Supplementary Angles –

angles that share a common vertex and ray…angles that are back to back.

*Vertex – the “corner” of the angle

*Ray – a line that has an endpoint

on one end and goes on

forever in the other direction.

Congruent Angles –

Angles with equal measurement

A ≅B denotes that A is congruent to B.

Transversal -

a line that intersects a set of parallel lines

t

Vertical Angles

Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles.

t

• 14
• 2  3

1

2

4

3

Vertical Angles

Find the measures of the missing angles

t

125 

?

125 

55 

?

55 

t

1

2

4

3

6

5

7

8

Linear Pair

Two adjacent angles that form a line. They are supplementary. (angle sum = 180)

• 1+2=180
• 2+4=180
• 4+3=180
• 3+1=180
• 5+6=180
• 6+8=180
• 8+7=180
• 7+5=180
Supplementary Angles/Linear Pair

Find the measures of the missing angles

t

?

108 

72 

180 - 72

?

108 

1

2

3

4

5

6

7

8

Corresponding Angles

Two angles that occupy corresponding positions when parallel lines are intersected by a transversal…same side of transversal AND same side of own parallel line. Corresponding angles are congruent angles.

t

• 15
• 2  6
• 3  7
• 4  8

Top Left

Top Right

Bottom Left

Bottom Right

Top Left

Top Right

Bottom Left

Bottom Right

Corresponding Angles

Find the measure of the missing angle

t

145 

35 

?

145 

Alternate Interior Angles

Two angles that lie between parallel lines on opposite sides of the transversal. These angles are congruent.

t

• 3  6
• 4  5

1

2

3

4

5

6

7

8

Alternate InteriorAngles

Find the measure of the missing angle

t

82 

82 

98 

?

Alternate Exterior Angles

Two angles that lie outside parallel lines on opposite sides of the transversal. They are congruent.

t

• 2  7
• 1  8

1

2

3

4

5

6

7

8

Alternate ExteriorAngles

Find the measure of the missing angle

t

120 

?

120 

60 

Same Side Interior Angles

Two angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary.

t

• 3 +5 = 180
• 4 +6 = 180

1

2

3

4

5

6

7

8

*Also known as Consecutive Interior Angles

Same Side InteriorAngles

Find the measure of the missing angle

t

180 - 135

135 

45 

?

Same Side Exterior Angles

Two angles that lie outside parallel lines on the same side of the transversal. These angles are supplementary.

t

• 1 +  7 = 180
• 2 + 8 = 180

1

2

3

4

5

6

7

8

*Also known as Consecutive Exterior Angles

Same Side ExteriorAngles

Find the measure of the missing angle

t

135 

180 - 135

?

45 

1,5

3,7

2,6

4,8

3,6

5,4

1,8

2,7

3,5

4,6

1,7

2,8

equivalent

equivalent

equivalent

supplementary

supplementary

112º

68º

68º

112º

112º

112º

68º

68º

Closing

What is a transversal?

Name the types of equivalent angles.

Name the types of supplementary angles.