ENGAGE! • Please complete the discovery worksheet on pairs of lines and angles – please get patty paper, straight edge and a protractor

Tell me about parallel lines

• Where do you see them?

• What use do they serve?

• What about perpendicular lines?

• Perpendicular lines ⊥ • lines that form right angles • ⊥ lines opposite reciprocal slopes

(product = -1)

• Oblique lines - intersecting lines that are not ⊥ • Skew lines - noncoplanar, nonparallel lines

that don’t intersect.

13

31 −and

45

54 and−

Intersecting lines

• lines with different slopes • lines that have a single common point

C

A

E

D

F

H

G

B

AD & EH are _______________. AD & FG are _______________. AD & AE are _______________. AD & HG are _______________.

parallel

parallel

perpendicular

skew

Know your angles!!!

1 2 3 4

5 6 7 8

Vertical angles Linear Pairs

Supplementary angles

Interior angles

Exterior angles 9 10 11 12

3.1 Identify Pairs of Lines and Angles

3.1-3.3 Parallel Lines and their Transversals

Transversal – a line that intersects two or

more coplanar lines at different points.

t

Corresponding Angles (C) – have corresponding

positions. For example: label ∠2 and ∠ 6

t

2

6

Corresponding Angles (C)

What shape do corresponding angles make?

t

2

6 F

Alternate Interior Angles (AI) – lie on alternate

(opposite) sides of the transversal on the interior (inside/between) the two lines. For example: label ∠ 4 and ∠5

t

4

5

Alternate Interior Angles (AI)

What shape do alternate interior angles make?

t

4

5

Z

Alternate Exterior Angles (AE) – lie on alternate

(opposite) sides of the transversal and on the exterior (outside) of the two lines. For example: label ∠1 and ∠8

t

1

8

Alternate Exterior Angles (AE)

Do alternate exterior angles have a shape?

t

1

8

Not really

Same Side Interior Angles (SSI) – lie on the same

side of the transversal and on the (inside) of the two lines. For example: label ∠3 and ∠ 5

t

3

5

Same Side Interior Angles (SSI)

What shape do Same Side Interior angles make?

t

3

5

C

Don’t forget!!!

Vertical Angles (V) Linear Pair (LP)

1 2 3 4

X shape Slanty T shape

Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.

1. ∠4 and ∠7 1 2 3 4 5 6

7 8 9 10 11 12 13 14

Same-Side Interior

Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.

2. ∠6 and ∠9 1 2 3 4 5 6

7 8 9 10 11 12 13 14

Alternate Interior

Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.

3. ∠6 and ∠14 1 2 3 4 5 6

7 8 9 10 11 12 13 14

Corresponding

Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.

4. ∠9 and ∠10 1 2 3 4 5 6

7 8 9 10 11 12 13 14

Linear Pair

Determine if the angles are alternate interior, same-side interior, corresponding, vertical angles, linear pair or no relationship.

5. ∠3 and ∠7 1 2 3 4 5 6

7 8 9 10 11 12 13 14

No Relationship

How does angle 9 relate to the other angles?

4 1 3 2 10 9

11 12

8

7 5

6

In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.

2x + 5 = 65

x = 30

m<3 = 65

m<4 = 115

What angle relationships can you use?

In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.

m<1 = 50 m<2 = 60

m<3 = 60

m<4 = 70

In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.

2x = 60 x = 30

5y + 2 = 60

y = 11.6 60

In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.

x + y = 30 x - y = 150

2x = 180 x = 90

x + y=30 90 +y = 30

Y = -60

150

In-Class Practice Find the value of the variables and the measure of each numbered angle given the set of parallel lines.

x = 60

y = 130

z = 60

In-Class Practice What two lines, if any, are parallel if the given information is true: a. m<1 = m<4 b. m<6 = m<4 c. m<2 + m<3 = m<5 d. m<2 + m<3 + m<5 = 180º f. <5 and <6 are supplementary e. <6 ≅ <8 g. <5 is supplementary to <8

t and r

m and n

t and r

none

t and r

m and n

none

Got it?

• Elaborate ws

Practice Evaluate WS