Properties of Parallel Lines
Standard
G.CO.9 Prove theorems about lines and angles. Theorems include when a transversal crosses parallel lines, alternate interior angles, etc.
Goals for this section:
Students should be able to identify alternate interior, same-side interior, alternate exterior, and corresponding angles and know their properties when looking at them with two parallel lines crossed by a transversal.
Same-Side Interior Angles Postulate
∠a + ∠b = 180°
Remember, same-side means it's on the same side of the transversal. Interior means that the angles are on the inside.
Alternate Interior Angles Theorem
∠a = ∠b
Alternate means that they're on different sides of the transversal and they are not next to each other. Interior means that the angles are on the inside.
Corresponding Angles Theorem
∠a = ∠b
Corresponding means that they're in the same "relative position". For this example, a and b are in the "bottom right corners".
Alternate Exterior Angles Theorem
∠a = ∠b
Alternate means that they're on different sides of the transversal and they are not next to each other. Exterior means to be on the outside.
