Geometry: Parallel Lines, Angles, and Theorems for Students

Alternate Exterior Angles

Outside the lines, opposite sides of the transversal. Equal if lines are parallel. m∠A = m∠B

Alternate Interior Angles

Inside the lines, opposite sides of the transversal. Equal if lines are parallel. m∠A = m∠B

Complementary Angles

Two angles that add up to a right angle. m∠1 + m∠2 = 90°

Supplementary Angles

Two angles that add up to a straight line. m∠1 + m∠2 = 180°

Perpendicular Lines

Lines that make four right angles. Each angle = 90°

Same-Side Exterior Angles

Outside the lines, same side of transversal. Supplementary if lines are parallel. m∠1 + m∠2 = 180°

Same-Side Interior Angles

Inside the lines, same side of transversal. Supplementary if lines are parallel. m∠1 + m∠2 = 180°

Corresponding Angles

Same position on the lines (top-left with top-left). Equal if lines are parallel. m∠A = m∠B

Vertical Angles

Two angles forming a straight line. m∠1 + m∠2 = 180°

Angle Bisector Theorem

A line splits an angle into two equal angles. m∠1 = m∠2

Alternate Interior Angles Theorem

Alternate interior angles are equal if lines are parallel. m∠A = m∠B

Alternate Exterior Angles Theorem

Alternate exterior angles are equal if lines are parallel. m∠A = m∠B

Same-Side Interior Angles Theorem

Same-side interior angles are supplementary if lines are parallel. m∠1 + m∠2 = 180°

Same-Side Exterior Angles Theorem

Same-side exterior angles are supplementary if lines are parallel. m∠1 + m∠2 = 180°

Perpendicular Lines Theorem

Perpendicular lines make four right angles. Each angle = 90°