3-1 Lines and AnglesGeometry

LINES AND ANGLES

Warm Up

2) 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?

Warm Up

9 -1

====

=Solve the equation:

-0.8 -20

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.

Formative

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

Lines that do not intersect

• Notation: l || m AB || CD

lm A

B

C

D

Examples of Parallel Lines

• Opposite sides of windows, desks, etc.

• Parking spaces in parking lots

• Parallel Parking

• Streets in a city block

PERPENDICULAR LINES

Lines that intersect to form a right angle

• Notation: m n

• Key Fact: 4 right angles are formed.

m

n

Ex. of Perpendicular Lines

any angle less than 90ºAcute Angle –

a 90º angleRight Angle –

any angle larger than 90ºObtuse Angle -

angles that add up to 90ºComplementary Angles –

angles that add up to 180ºSupplementary 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.

Congruent Angles – Angles with equal measurement

A ≅ B denotes that A is congruent to B.

Transversal -

t

a line that intersects a set of parallel lines

Vertical Angles

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

1 2

3 4

t

1 42 3

Vertical Angles

Find the measures of the missing angles

125

?

?

55

t

55

125

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

1 2

3 4

5 6

7 8

t

Linear Pair

5+6=1806+8=1808+7=1807+5=180

1+2=1802+4=1804+3=1803+1=180

Supplementary Angles/Linear Pair

Find the measures of the missing angles

? 72

?

t

108

108 180 - 72

Corresponding AnglesTwo 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.

Top Left

t

Top Left

Top Right

Top Right

Bottom Right

Bottom Right

Bottom Left

Bottom Left

1 52 63 74 8

1 2

3 4

5 6

7 8

Corresponding Angles

Find the measure of the missing angle

145

?

t

35

145

Alternate Interior Angles

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

t

3 64 5

1 2

3 4

5 6

7 8

Alternate Interior Angles

Find the measure of the missing angle

82

?

t

98 82

Alternate Exterior Angles

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

t

2 71 8

1 2

3 4

5 6

7 8

Alternate Exterior Angles

Find the measure of the missing angle

120

?

t

60 120

Same Side Interior AnglesTwo angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary.

t

3 +5 = 1804 +6 = 180

1 2

3 4

5 6

7 8

*Also known as Consecutive Interior Angles

Same Side Interior Angles

Find the measure of the missing angle

?

t

135

45

180 - 135

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 = 1802 + 8 = 180

1 2

3 4

5 6

7 8

*Also known as Consecutive Exterior Angles

Same Side Exterior Angles

Find the measure of the missing angle

?

t

135

45

180 - 135

1,5 4,82,63,7

5,43,6

2,71,8

4,63,5

2,81,7

equivalent

equivalent

equivalent

supplementary

supplementary

112º

112º68º

112º68º

68º

68º

112º

Closing

What is a transversal?

Name the types of equivalent angles.

Name the types of supplementary angles.