Angles and Parallel Lines
When a transversal line crosses two parallel lines, it creates pairs of angles with special relationships. Understanding these angle properties is essential for geometric reasoning and proofs.
What You Need to Know
Key Concept Diagram
Alternate angles are equal (they form a Z-shape between parallel lines)
Co-interior (same-side interior) angles add up to 180 degrees (they form a C-shape)
Corresponding angles are equal (they form an F-shape)
Vertically opposite angles are equal (formed by two intersecting lines)
Angles on a straight line add up to 180 degrees; angles around a point add up to 360 degrees
Key Vocabulary
Transversal
A line that crosses two or more other lines
Alternate Angles
Angles on opposite sides of a transversal between parallel lines; they are equal (Z-angles)
Corresponding Angles
Angles in the same position at each intersection of parallel lines and a transversal; they are equal (F-angles)
Co-interior Angles
Angles on the same side of the transversal between parallel lines; they add to 180 degrees (C-angles)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Two parallel lines are cut by a transversal. One alternate angle is 65 degrees. What is the other alternate angle?
Question 2
Two parallel lines are cut by a transversal. One co-interior angle is 110 degrees. What is the other co-interior angle?
Question 3
Two lines intersect. One angle is 42 degrees. What is the vertically opposite angle?
Key Concepts Summary
- ●Alternate angles are equal (they form a Z-shape between parallel lines)
- ●Co-interior (same-side interior) angles add up to 180 degrees (they form a C-shape)
- ●Corresponding angles are equal (they form an F-shape)
- ●Vertically opposite angles are equal (formed by two intersecting lines)
- ●Angles on a straight line add up to 180 degrees; angles around a point add up to 360 degrees