Lesson 48 Fall 2022 Parallel Lines and Transversals

3

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by
transversals? APPLICATION PRACTICE

Lesson Objectives:

Our Amazing Students will be able to…

1)

Apply properties of special angles to identify angles
formed by parallel lines cut by a transversal?

2)

Analyze diagrams to determine what algebraic
equation to apply when proving lines parallel lines?

4

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by
transversals? APPLICATION PRACTICE

Remember to turn on Nearpod Notes!

1. We are going to have a quick review

of the properties of angles formed by
parallel lines cut by transversals.

2. You will work with a partner, or

independently, to solve related
problems.

3. Teachers will circulate and assist,

though you must try to solve the
problems yourself first.

5

Remember these words?

Complementary Angles –

Supplementary Angles –

Vertical Angles –

Parallel Lines –

Congruent –

What is the angle measure of a straight
line?

2 angles that = 90°

2 angles that = 180°

2 angles across the vertex

2 lines that never touch

Geometry word for equal ( )

180°

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

6

Think About these words!!

Alternate – opposite or different

Consecutive – in a row or same side

Exterior – outside

Interior – inside

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Transversal

When a transversal t intersects line n and m,
angles of the following types are formed:

●

Vertical angles

●

Linear Pairs

●

Consecutive interior angles

●

Alternate interior angles

●

Consecutive exterior angles

●

Alternate exterior angles

●

Corresponding angles

t

m

n

Definition:A line that intersects two or more lines in a
plane at different points is called a transversal.

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Vertical Angles

Two angles in the same group that are across the vertex from
each other. These angles are congruent.

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Linear Pair

● Linear Pair:
Two angles in the same group that are side-by-side. A Linear
Pair is supplementary [angles that form a line (sum = 180°)].

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Consecutive Interior Angles

Consecutive Interior Angles: Two angles in a different groups ,

inside the parallel lines and are on the same side of the
transversal. These angles are supplementary (=180°).

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Alternate Interior Angles

● Alternate Interior Angles: Two angles that are in different

groups , inside the parallel lines and are on different sides of the
transversal. These angles are congruent.

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Consecutive Exterior Angles

● Consecutive Exterior Angles: Two angles in different

groups, outside the parallel lines and are on the same side
of the transversal. These angles are supplementary
(= 180°).

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Alternate Exterior Angles

● Alternate Exterior Angles: Two angles in different

groups, outside the parallel lines and are on different
sides of the transversal. The angles are congruent.

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Corresponding Angles

Corresponding Angles: Two angles in different groups,

but in the same position in their group. One angle is
inside the parallel lines and the other angle is outside of
the parallel lines. These angles are congruent.

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Angles and Parallel Lines

●
If two parallel lines are cut by a transversal, then the following
pairs of angles are congruent.

1.
Corresponding angles

2.
Alternate interior angles

3.
Alternate exterior angles

●
If two parallel lines are cut by a transversal, then the following
pairs of angles are supplementary.

1.
Consecutive interior angles

2.
Consecutive exterior angles

3.
Linear Pair

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

AIM: How can we prove and solve angle pairs resulting from parallel lines cut by transversals?
APPLICATION PRACTICE

Work with a
partner, or
independently, to
complete the front
and back of this
problem set.

Multiple Choice

$$\angle1$$  and  $$\angle4$$  are

• Corresponding

• Vertical Angles

• Alternate Interior

• Supplementary

Multiple Choice

$$\angle1$$  and  $$\angle4$$  are

• Corresponding

• Vertical Angles

• Alternate Interior

• Supplementary

Multiple Choice

Angle A and C are...

• Supplementary

• Congruent

Multiple Choice

Find the measure of the missing angle.

• 48

• 84

• 132

Multiple Choice

Angle Q and B are...

• Alternate Interior Angles
• Consecutive Interior Angles
• Corresponding Angles
• Alternate Exterior Angles

Multiple Choice

Find the missing angle

• 108

• 92

• 88

Multiple Choice

Angle S and A are...

• Alternate Interior Angles
• Consecutive Interior Angles
• Corresponding Angles
• Alternate Exterior Angles

Multiple Choice

Angles 4 and 6 are same-side interior, so they are...?

• Supplementary

• Congruent

Multiple Choice

Find C 

• ∠C=116°
• ∠C=64°
• ∠C=180°
• ∠C=26°

Multiple Choice

Find the missing angle measure.

• Not enough information

• 131

• 49

Multiple Choice

Angles 4 and 6 are...

• supplementary

• congruent

Multiple Choice

Solve for x.

• 180

• 12

• 8

• 16.7

Multiple Choice

Which pair of angles must be supplementary so that r is parallel to s?

• ∠2 and ∠3
• ∠5 and ∠6
• ∠4  and ∠10
• ∠6  and ∠14

Multiple Choice

Solve for x.

• 23

• -20

• 32

• 20

Multiple Choice

Line v is a transversal.  Which is a true statement?

• w // x and x // y
• w // x and y // z
• w // y and x // z
• w // z and x // y

Multiple Choice

$$\angle7\cong\angle2$$  True or false?

• True

• False

Multiple Choice

Which condition will prove that line l is parallel to line m?

• ∠1 ≅ ∠3

• ∠3 ≅ ∠5

• ∠1 ≅ ∠6

• ∠6 ≅ ∠5

Multiple Choice

Find the missing angle.

• 39

• 51

• 129

• 139

Multiple Choice

Which condition will prove that line l is parallel to line m?

• ∠1 ≅ ∠3

• ∠3 ≅ ∠5

• ∠1 ≅ ∠6

• ∠6 ≅ ∠5

Multiple Select

SELECT ALL THAT APPLY

If two angles are same-side exterior, they are:

• Supplementary

• Congruent

• Add to 180

• Equal

Multiple Select

Which statements are true? Select all that apply.

• Vertical angles are congruent.

• Corresponding Angles are Supplementary.

• Parallel Angles are Congruent.

• Alternate Interior Angles are Congruent.

Multiple Choice

$$\angle1$$  and  $$\angle5$$  are corresponding angles. If  $$\angle1$$  is 95 degrees, how much is  $$\angle5?$$  

• 95

• 85

Multiple Choice

Solve for x. Then find the measure of the missing angle.

• x = 18
  $$60\degree$$
  

• x = 60
  $$120\degree$$
  

Multiple Choice

$$\angle5=130\degree$$
Find the measure of angle 3.

• 5

• 130

• 50

Multiple Choice

Angles 4 and 8 are...

• Corresponding and supplementary

• Same side interior and supplementary

• Corresponding and congruent

• Same side exterior and congruent