Types of angles

Learning Objectives Identify and name corresponding, alternate interior, alternate exterior, and consecutive interior angles. Apply the properties of angles formed by a transversal intersecting parallel lines to find unknown angle measures. Solve multi-step algebraic equations derived from angle pair relationships. Use the converses of angle pair theorems to prove that two lines are parallel. Define and apply the properties of angles formed by perpendicular lines. Construct logical arguments to justify geometric claims about angle relationships. Ever noticed the perfect 'Z' shape in a city's street grid or the parallel lines of a railway track? 🏙️ The angles created in these patterns follow predictable, powerful rules. This tutorial explores the special angle...

TermDefinitionExample TransversalA line that intersects two or more coplanar lines at distinct points.In a diagram with lines 'l' and 'm', a third line 't' that crosses both 'l' and 'm' is the transversal. Corresponding AnglesA pair of angles that are in the same relative position at each intersection where a transversal crosses two lines. Think of them as being in the 'same corner'.If a transversal cuts two lines, the angle in the top-left of the first intersection and the angle in the top-left of the second intersection are corresponding angles. Alternate Interior AnglesA pair of angles on opposite sides of the transversal and located *between* the other two lines. They form a 'Z' or 'S' shape.If a transvers...

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. If l || m, then ∠1 ≅ ∠5. Use this rule to set the measures of corresponding angles equal to each other when you know the lines are parallel. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. If l || m, then ∠3 ≅ ∠6. Use this theorem to set the measures of alternate interior angles equal to each other when you know the lines are parallel. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. If l || m, then m∠3 + m∠5 = 180°. Use this theorem when you have...