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

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

(Type only the value in the blank.)

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