21. Parallel Lines cut by a Transversal

Parallel Lines

Remember, PARALLEL LINES are lines that lie in the same plane and do not intersect.

Transversal

A TRANSVERSAL is a line that intersects two or more lines at distinct points.

Parallel Lines & Transversals

When a TRANSVERSAL intersects PARALLEL LINES, 8 angles are formed.

These angles have special realtionships that are helpful to remember.

Multiple Choice

Which figure shows a set of parallel lines?

• Figure 1

• Figure 2

• Figure 3

• Figure 4

Multiple Choice

True or False: This figure shows a picture of a transversal.

• True, the transversal goes from the top left to bottom right.

• True, the transversal goes from the top right to bottom left.

• False, this is a picture of intersecting lines.

The 8 angles formed by two parallel lines and a transversal create the following special angle pairs:

• Corresponding Angles

• Vertical Angles

• Consecutive Interior Angles

• Consecutive Exterior Angles

• Alternate Interior Angles

• Alternate Exterior Angles

Corresponding Angles

Just like corresponding parts of similar figures, CORRESPONDING ANGLES are in the same position on each parallel line.

These angle pairs are CONGRUENT.

And have the same degrees.

Vertical Angles

VERTICAL ANGLES are pairs of opposite angles formed by intersecting lines.

These angle pairs are CONGRUENT.

x and x are vertical angles and are the same degrees

y and y are vertical angles and are the same degreees

Multiple Choice

What angle corresponds to $$\angle1$$ ?

Note: Look at angle one in the first intersection...

Which angle is in the same place in the second intersectionn.

• $$\angle7$$

• $$\angle5$$

• $$\angle3$$

• $$\angle2$$

Multiple Choice

Which angles are vertical angles?

Look for angles on opposite sides of the intersections.

• $$\angle5\ and\ \angle3$$

• $$\angle2\ and\ \angle4$$

• $$\angle1\ and\ \angle4$$

• $$\angle6\ and\ \angle4$$

Interior vs. Exterior

Angles in between the parallel lines (in the white area) are called INTERIOR ANGLES.

Angles that are outside of the parallel lines (in the blue areas) are EXTERIOR ANGLES.

Consecutive vs. Alternate

CONSECUTIVE angles are on the SAME SIDE of the transversal.

ALTERNATE angles are on OPPOSITE SIDES of the transversal.

Consecutive Interior Angles

Angles on the SAME SIDE of the transversal and INSIDE of the parallel lines.

These angles are SUPPLEMENTARY ANGLES. (they add up to 180⁰)

Consecutive Exterior Angles

Angles on the SAME SIDE of the transversal and OUTSIDE of the parallel lines.

These angles are SUPPLEMENTARY ANGLES.

Alternate Interior Angles

Angles on the OPPOSITE SIDES of the transversal and INSIDE of the parallel lines.

These angles are CONGRUENT.

They have the same degrees.

Alternate Exterior Angles

Angles on the OPPOSITE SIDES of the transversal and OUTSIDE of the parallel lines.

These angles are CONGRUENT.

(They have the same degrees)

Angle Relationships and Parallel Lines

Day 2 - Parallel Lines and Transversals

Multiple Choice

∠3 and ∠6 are...

• Supplementary angles

• Vertical angles

• Corresponding angles

• Alternate interior angles

Multiple Choice

Angle B and Angle R are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Angle C and Angle P are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Name the consecutive exterior interior angle to angle 1.

• 4

• 5

• 6

• 8

We can use the relationships of these angle pairs to find the measure of missing angles.

Multiple Choice

If the  $$m\angle1\ =\ 57\degree,$$  find the measure of  $$\angle5$$ ?

• $$123\degree$$  

• $$57\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Find y.

• 50

• 130

• 180

• 45

Multiple Choice

Find the value of x.

• x = 100

• x = 47

• x = 90

• x = 133

Multiple Choice

What is the measure of ∠6?

• 55

• 155

• 45

• 135

Multiple Choice

What is the measure of ∠1?

• 55

• 155

• 135

• 45

Multiple Choice

What is the measure of $$\ \angle A$$  ?

• 82°

• 98°

• 180°

• 8°

Step 2: Write the equation to solve.

Multiple Choice

Which is not an example of parallel lines?

Multiple Choice

Two lines going the exact same way and will never intersect

• Alternate exterior angles

• Parallel lines

• Alternate interior angles

• Vertical lines

Multiple Choice

Name the angle relationship.

• Alternate Interior

• Alternate Exterior

• Corresponding

• Vertical Angles

Multiple Choice

Angles on the same side of a transversal, in corresponding positions, and are congruent are called _____.

• Vertical angles

• Corresponding Angles

• Supplementary Angles

• Alternate Interior Angles

Multiple Choice

Angle S and A are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Angle C and P are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Name the corresponding angle to angle 4.

• angle 8

• angle 6

• angle 2

• angle 5