Parallel Lines

Parallel Lines

by Erica Player

​When parallel lines are cut by a transversal...

​There will be 8 angles total.

All the yellow angles are congruent.

All the blue angles are congruent.

Here's an example with angle measurements. When the lines are PARALLEL, there will only be 2 different angle measurements available!

​Do you see the vertical angles in this picture? There are 4 SETS of them.

*On the next slide, there will be questions about vertical angles.

Multiple Choice

Vertical angles are always

• acute

• total 180 degrees

• congruent (equal measures)

• adjacent angles

Multiple Choice

Which angle is a vertical angle to  $$\angle7$$  ?

• $$\angle5$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle9$$  

Multiple Choice

Given the two parallel lines cut by a transversal.

What is the vertical angle to angle 4?

• Angle 2

• Angle 6

• Angle 8

• Angle 7

Multiple Choice

Given the following two parallel lines that have been cut by a transversal.

True or False, $$\angle6$$  and $$\angle4$$  are vertical angles?

• True

• False

Fill in the Blanks

10)Given the two parallel lines cute by a transversal, What is the measure of  $\angle5$  ?

​Corresponding Angles

​If you trace CORRESPONDING ANGLES, they point in the same direction!

​When the lines are PARALLEL, these angles are also CONGRUENT.

​

​

​

​MORE EXAMPLES ON THE NEXT SLIDE...

​Here are 4 different sets of CORRESPONDING angles. Notice:

they are CONGRUENT!

​The CORRESPONDING angles are the same color

​

Multiple Choice

What angle corresponds to  $$\angle3$$  ?

• $$\angle4$$  

• $$\angle5$$  

• $$\angle8$$  

• $$\angle7$$  

Multiple Choice

What angle corresponds to  $$\angle1$$  ?

• $$\angle4$$  

• $$\angle5$$  

• $$\angle8$$  

• $$\angle2$$  

Multiple Choice

What angle corresponds to $$\angle4$$ ?

• $$\angle4$$

• $$\angle5$$

• $$\angle3$$

• $$\angle2$$

Multiple Choice

What is the angle relationship between the indicated angles in the diagram?

• Alternate Interior Angles

• Alternate Exterior Angles

• Corresponding Angles

• Vertical Angles

• Linear pair

​ALTERNATE INTERIOR ANGLES

​NOTICE: there are always 2 sets of these.

​See the yellow set and the blue set?

​Another example:

​Their measures are equal!

​

​x = x

​

​y = y

Multiple Choice

Angle 3 and Angle 6 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

Multiple Choice

Name the alternate interior angle to angle 3.

• 4

• 5

• 6

• 8

Multiple Choice

3) Given the following two parallel lines cut by a transversal.

Which pair of angles represents alternate interior angles?

• $$\angle3$$  and $$\angle8$$  

• $$\angle7$$  and $$\angle2$$  

• $$\angle7$$  and $$\angle8$$  

• $$\angle4$$  and $$\angle8$$  

Alternate Exterior Angles​

​There will always be 2 sets of these. Look at the picture --->

​Another example:

Multiple Choice

If the  $$m\angle7\ =\ 115\degree,$$  find the measure of  $$\angle2.$$  

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Name the angle relationship.

• Alternate Interior

• Alternate Exterior

• Corresponding

• Vertical Angles

​All the angles so far have been CONGRUENT. Let's look at some that are NOT congruent.

​CONSECUTIVE INTERIOR. These angles cannot be the same because one is ACUTE and one is OBTUSE

​More examples of CONSECUTIVE INTERIOR:

​

​These are NOT congruent. They ADD to 180. Do you remember the vocabulary word for this???

​

​SUPPLEMENTARY!

​113 + 67 = 180

Multiple Choice

Angle C and P are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

If the  $$m\angle4\ =\ 60\degree,$$  find the measure of  $$\angle6.$$  

• $$60\degree$$  

• $$120\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

If the  $$m\angle5\ =\ 63\degree,$$  find the measure of  $$\angle3.$$  

• $$63\degree$$  

• $$117\degree$$  

• $$180\degree$$  

• Cannot be determined

​Summary: Any pair of angles in this diagram are either CONGRUENT (same measure) or SUPPLEMENTARY (add up to 180)

​PART = PART

​ 60 = 60

​

​PART + PART = WHOLE

​ 60 + 120 = 180

One more thing to remember:

ANY OF THE ADJACENT ANGLES MAKE A LINEAR PAIR (ADD TO 180)

​DO YOU SEE ALL OF THE 60 AND 120

​ANGLES THAT ARE ADJACENT?

​Now, you will try some mixed practice. You can use your notes, and you can go backwards in the slideshow to see notes. Do your best! You will need a calculator.

​

Multiple Choice

Calculate the missing angle.

• 155º

• 35º

• 135º

• 145º

Multiple Choice

Calculate the missing angle.

• 132º

• 58º

• 48º

• 38º

Multiple Choice

Calculate the missing angle.

• 63º

• 43º

• 127º

• 53º

Multiple Choice

Find C 

• ∠C=116°

• ∠C=64°

• ∠C=180°

• ∠C=26°

Multiple Choice

Angle 1 and Angle 5 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

Multiple Choice

Which of the following angles would NOT be congruent to the measure of $$\angle7$$ ?

• $$\angle2$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle8$$  

Multiple Choice

Which of the following is an example of corresponding angles?

• $$\angle8\ and\ \angle4$$  

• $$\angle5\ and\ \angle7$$  

• $$\angle1\ and\ \angle7$$  

• $$\angle3\ and\ \angle5$$  

Multiple Choice

Which of these angles is NOT congruent to angle 5?

• Angle 6

• Angle 8

• Angle 1

• Angle 4

Multiple Choice

Angles 4 and 6 are...

• supplementary

• congruent

Multiple Choice

Angle 2 and $$\angle$$  ______ form a linear pair. 

• 1

• 3

• 5

• 7

Multiple Choice

If the  $$m\angle7\ =\ 115\degree,$$  find the measure of  $$\angle1.$$  

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Name the angle relationship.

• Alternate Interior Angles

• Alternate Exterior Angles

• Corresponding Angles

• Vertical Angles

Multiple Choice

Name the angle relationship.

• Alternate Interior Angles

• Alternate Exterior Angles

• Corresponding Angles

• Vertical Angles

Multiple Choice

Name the angle relationship.

• Alternate Interior Angles

• Alternate Exterior Angles

• Corresponding Angles

• Vertical Angles 

Multiple Choice

If angle P measures 60 degrees, what is the measure of angle C?

• 60^o

• 30^o

• 120^o

• 180^o

Multiple Choice

If angle P measures 50 degrees, what is the measure of angle Q?

• 50^o

• 40^o

• 130^o

• 180^o

Multiple Choice

What are supplementary angles?

• Two angles that add up to 180°

• Two angles that add up to 90°

• Angles that are equal to each other

• Angles that are opposite of each other when lines intersect

Multiple Choice

Line m is parallel to line n. Find the measure of ∠1.

• 65°

• 115°

• 125°

• 180°