Transversal of Parallel Lines

Lesson 3-1: Parallel Lines & Transversals

We give special names to the angle pairs formed by a transversal and the lines it intersects.​

(Study and copy these notes, including the diagram, then use them to answer the following questions.)

Multiple Choice

$$\angle1$$  and $$\angle2$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle1\$$ and  $$\angle2$$    are __.

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle1\$$ and $$\angle2$$  are ___.

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle1\$$  and $$\angle2$$  are ___.

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle8$$  and  $$\angle6$$   are __.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle3$$  and  $$\angle7$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle3\$$  and  $$\angle2$$   are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle7\$$  and $$\angle5$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle4$$  and $$\angle8$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle5$$  and $$\angle6$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle5$$ and $$\angle6$$ are ___.

• Alternate Interior Angles

• Alternate Exterior Angles

• Vertical Angles

• Corresponding Angles

• Linear Pair

Multiple Choice

$$\angle1\$$  and $$\angle4$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

$$\angle1\$$  and $$\angle5$$  are ___.  

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

• None of these

Multiple Choice

Which of the angle pairs below is a pair of corresponding angles?  

• $$\angle8$$  and  $$\angle6$$  

• $$\angle2\$$  and  $$\angle6$$  

• $$\angle2\$$  and  $$\angle3$$  

• $$\angle8\$$  and  $$\angle5$$  

Multiple Choice

Which of the angle pairs below is a pair of same-side interior angles?  

• $$\angle7\$$  and  $$\angle6$$  

• $$\angle2\$$  and  $$\angle6$$  

• $$\angle2\$$  and  $$\angle4$$  

• $$\angle8\$$  and  $$\angle5$$  

Multiple Choice

Which of the angle pairs below is a pair of alternate exterior angles?  

• $$\angle7\$$  and  $$\angle6$$  

• $$\angle2\$$  and  $$\angle6$$  

• $$\angle2$$  and  $$\angle4$$  

• $$\angle1\$$  and  $$\angle5$$  

Multiple Choice

Which of the angle pairs below is a pair of corresponding angles?  

• $$\angle7$$  and  $$\angle5$$  

• $$\angle2\$$  and  $$\angle6$$  

• $$\angle2\$$  and  $$\angle8$$  

• $$\angle1\$$  and  $$\angle5$$  

Multiple Choice

Which of the angle pairs below is a pair of alternate interior angles?  

• $$\angle7\$$  and  $$\angle5$$  

• $$\angle3\$$  and  $$\angle7$$  

• $$\angle4$$  and  $$\angle8$$  

• $$\angle1\$$  and  $$\angle3$$  

Multiple Choice

Which of the angle pairs below are a linear pair?  

• $$\angle7\$$  and  $$\angle5$$  

• $$\angle3\$$  and  $$\angle6$$  

• $$\angle4$$  and  $$\angle8$$  

• $$\angle2$$  and  $$\angle3$$  

Multiple Choice

Which of the angle pairs are vertical angles?  

• $$\angle7\$$  and  $$\angle5$$  

• $$\angle3\$$  and  $$\angle5$$  

• $$\angle4$$  and  $$\angle8$$  

• $$\angle2$$  and  $$\angle1$$  

​When the lines cut by a transversal are parallel lines, the measures of the angles in each pair have specific relationships.

Here is the first (considered a postulate):

​(In the diagram at left, the corresponding angles are the ones marked with the same color.)

​Using the Corresponding Angles Postulate (from the previous slide), it is possible to prove the following other relationships (considered theorems):

​Note: Same-side (consecutive) exterior angles are also supplementary, but this is not always given a name as a theorem. Nonetheless, you may use it to solve problems.

​**(Copy these theorems into your notes. Make sure you include their names! You will use all of them to answer the following questions.)**

Multiple Choice

Which two angles are supplementary

• ∠1 and ∠3

• ∠2 and ∠6

• ∠4 and ∠6

• ∠7 and ∠8

Multiple Choice

Which two angles are alternate exterior?

• 1 & 3

• 2 & 6

• 4 & 7

• 7 & 1

Multiple Choice

Which of the following two angles are congruent?

• 1 & 4

• 4 & 5

• 1 & 5

• 7 & 8

Multiple Choice

If angle 2 is 70 degrees, what is the measure of angle 1?

• 70 degrees

• 20 degrees

• 110 degrees

• 180 degrees

Multiple Choice

If angle 2 is 70 degrees, what is the measure of angle 4?

• 70

• 110

• 20

• 180

Multiple Choice

Find x.

• 130
• 50

Multiple Choice

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

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Which of these angles is NOT congruent to angle 5?

• Angle 6
• Angle 8
• Angle 1
• Angle 4

Math Response

Write the equation you would need to solve in order to find x.

Type answer here

Correct Answer: 3x+20+2x=180

Deg^°

Rad

Fill in the Blanks

Math Response

Write the equation you would need to solve in order to find x.

Type answer here

Correct Answer: 8x-77=3x+38

Deg^°

Rad

Math Response

Use the equation you wrote in the previous problem to find the value of x.

(Enter only the value in the blank.)

Type answer here

Correct Answer: 23

Deg^°

Rad