3.3: Corresponding Angles
What if you were presented with two angles that are in the same place with respect to the transversal but on different lines? How would you describe these angles and what could you conclude about their measures? After completing this Concept, you'll be able to answer these questions using your knowledge of corresponding angles.
Watch This
CK12 Foundation: Chapter3CorrespondingAnglesA
Watch the portions of this video dealing with corresponding angles.
James Sousa: Angles and Transversals
Watch this video beginning at the 4:50 mark.
James Sousa: Corresponding Angles Postulate
James Sousa: Corresponding Angles Converse
Guidance
Corresponding Angles
are two angles that are in the “same place” with respect to the transversal, but on different lines. Imagine sliding the four angles formed with line
Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
If
Converse of Corresponding Angles Postulate: If corresponding angles are congruent when two lines are cut by a transversal, then the lines are parallel.
Investigation: Corresponding Angles Exploration
You will need: paper, ruler, protractor
 Place your ruler on the paper. On either side of the ruler, draw lines, 3 inches long. This is the easiest way to ensure that the lines are parallel.
 Remove the ruler and draw a transversal. Label the eight angles as shown.
 Using your protractor, measure all of the angles. What do you notice?
In this investigation, you should see that
Investigation: Creating Parallel Lines using Corresponding Angles

Draw two intersecting lines. Make sure they are not perpendicular. Label them
l andm , and the point of intersection,A , as shown. 
Create a point,
B , on linem , aboveA . 
Copy the acute angle at
A (the angle to the right ofm ) at pointB . See Investigation 22 in Chapter 2 for the directions on how to copy an angle. 
Draw the line from the arc intersections to point
B .
From this construction, we can see that the lines are parallel.
Example A
If
Example B
If
Example C
Using the picture above, list pairs of corresponding angles.
Corresponding Angles:
Watch this video for help with the Examples above.
CK12 Foundation: Chapter3CorrespondingAnglesB
Vocabulary
Corresponding Angles are two angles that are in the “same place” with respect to the transversal, but on different lines.
Guided Practice
Lines
1. If
2. If
3. If
Answers:
1. Since they are corresponding angles and the lines are parallel, they must be congruent. Set the expressions equal to each other and solve for
2. Since they are corresponding angles and the lines are parallel, they must be congruent. Set the expressions equal to each other and solve for
3. Since they are corresponding angles and the lines are parallel, they must be congruent. Set the expressions equal to each other and solve for
Practice

Determine if the angle pair
∠4 and∠2 is congruent, supplementary or neither:  Give two examples of corresponding angles in the diagram:

Find the value of
x :  Are the lines parallel? Why or why not?
 Are the lines parallel? Justify your answer.
For 610, what does the value of

If
m∠1=(6x−5)∘ andm∠5=(5x+7)∘ . 
If
m∠2=(3x−4)∘ andm∠6=(4x−10)∘ . 
If
m∠3=(7x−5)∘ andm∠7=(5x+11)∘ . 
If
m∠4=(5x−5)∘ andm∠8=(3x+15)∘ . 
If
m∠2=(2x+4)∘ andm∠6=(5x−2)∘ .
For questions 1115, use the picture below.

What is the corresponding angle to
∠4 ? 
What is the corresponding angle to
∠1 ? 
What is the corresponding angle to
∠2 ? 
What is the corresponding angle to
∠3 ?  Are the two lines parallel? Explain.
Image Attributions
Description
Learning Objectives
Here you'll learn what corresponding angles are and their relationship with parallel lines.