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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.

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3-1 Lines and Angles Geometry


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warm up
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 up1
Warm Up

Solve the equation:

=

-20

=

-0.8

=

9

=

=

-1

slide5

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
Essential Questions

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

parallel lines

B

A

D

l

C

m

PARALLEL LINES

Lines that do not intersect

  • Notation:l || mAB|| CD
slide9

Examples of Parallel Lines

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

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 90
any angle less than 90º

Acute Angle –

a 90 angle
a 90º angle

Right Angle –

angles that add up to 90
angles that add up to 90º

Complementary Angles –

angles that add up to 180
angles that add up to 180º

Supplementary Angles –

adjacent angles
Adjacent 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.

slide18

Congruent Angles –

Angles with equal measurement

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

transversal
Transversal -

a line that intersects a set of parallel lines

t

vertical angles
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 angles1
Vertical Angles

Find the measures of the missing angles

t

125 

?

125 

55 

?

55 

linear pair

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
Supplementary Angles/Linear Pair

Find the measures of the missing angles

t

?

108 

72 

180 - 72

?

108 

corresponding angles

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 angles1
Corresponding Angles

Find the measure of the missing angle

t

145 

35 

?

145 

alternate interior angles
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 interior angles1
Alternate InteriorAngles

Find the measure of the missing angle

t

82 

82 

98 

?

alternate exterior angles
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 exterior angles1
Alternate ExteriorAngles

Find the measure of the missing angle

t

120 

?

120 

60 

same side interior angles
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 interior angles1
Same Side InteriorAngles

Find the measure of the missing angle

t

180 - 135

135 

45 

?

same side exterior angles
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 exterior angles1
Same Side ExteriorAngles

Find the measure of the missing angle

t

135 

180 - 135

?

45 

slide34

1,5

3,7

2,6

4,8

3,6

5,4

1,8

2,7

3,5

4,6

1,7

2,8

slide35

equivalent

equivalent

equivalent

supplementary

supplementary

slide36

112º

68º

68º

112º

112º

112º

68º

68º

closing
Closing

What is a transversal?

Name the types of equivalent angles.

Name the types of supplementary angles.