Properties of Parallel Lines Geometry Unit 3, Lesson 1 Mrs. King

Angles Formed by a Transversal Transversal – a line that intersects two lines t L M

Corresponding Angles Two angles are corresponding angles if they occupy corresponding positions, such as t L M

Alternate Interior Angles Two angles are alternate interior angles if they lie between L and M on opposite sides of t, such as t L M

Alternate Exterior Angles Two angles are alternate exterior angles if they lie outside L and M on opposite sides of t, such as t L M

Same-Side-Interior Angles Two angles are consecutive interior angles if they lie between L and M on the same side of t, such as t L M

Transitive Property If a=b and b=c, then a=c What does this remind you of?!

Example Given:  1   3 and  3   5 What can we conclude?  1   5 due to the Transitive Property

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent.  1   5  2   6  3   7  4   8

Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent.  2   8  3   5

Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.  1   7  4   5

Same-Side Interior Angles Theorem If two parallel lines are cut by a transversal, then same-side interior angles are supplements.  2 and  5 are supplementary  3 and  8 are supplementary

Find the measure of each angle given l || m. 42° l m

a = 65 c = 40 a + b + c = b + 40 = 180 b = 75 In the diagram above, l || m. Find the values of a, b, and c. Properties of Parallel Lines

Angles: