Alternate Interior Angles
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More Lessons for Grade 8 Math
Examples, solutions, videos, and worksheets to help Grade 8 students learn about alternate interior angles.
The Alternate Interior Angles Theorem
The most significant property of alternate interior angles relates to parallel lines:
If a transversal intersects two parallel lines, then the alternate interior angles are congruent (equal in measure).
The following diagram shows some examples of alternate interior angles. Scroll down the page for more examples and solutions.
Geometry Worksheets
Practice your skills with the following geometry worksheets:
Printable & Online Geometry Worksheets
Converse of the Alternate Interior Angles Theorem
The converse of this theorem is also true and is used to prove that lines are parallel:
If two lines are intersected by a transversal and a pair of alternate interior angles are congruent, then the two lines are parallel.
Key Points to Remember:
- Interior: They are between the two lines being cut.
- Alternate: They are on opposite sides of the transversal.
- Congruent (if lines are parallel): This is the crucial property for parallel lines. If the lines are not parallel, alternate interior angles will still be “alternate interior” by definition of their position, but they will not be equal.
- Z-Shape: A common visual trick to identify alternate interior angles is to look for a “Z” shape (or a backward “Z”) formed by the lines and the transversal. The angles in the “corners” of the “Z” are alternate interior angles.
Alternate Interior Angles
This video describes alternate interior angles are and their relationship with parallel lines.
Corresponding Angles and Same-Side Interior Angles
How to use alternate interior angles to find the measures of angles?
How to Find an Angle Using Alternate Interior Angles?
Alternate Interior Angles - Proof
A proof of the common geometric theorem showing that when lines are parallel, alternate interior angles are congruent.
Proof: Alternate Interior Angles Converse
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