PROPERTIES OF PARALLEL LINES. Transversal Line that intersect two coplanar lines at two distinct points Eight angles are formed by a transversal line.

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Presentation transcript:

PROPERTIES OF PARALLEL LINES

Transversal Line that intersect two coplanar lines at two distinct points Eight angles are formed by a transversal line

13 42 Alternate interior angles Angles inside the two lines on opposite sides of the transversal <3 and < 4 <1 and <2

13 42 Same side interior angles Angles inside the two lines on the same side of the transversal < 1 and < 4 < 2 and < 3

Corresponding angles Angles that are in similar positions on the same side of a transversal <2 and <6 <5 and < 4 <1 and <7 <3 and <8

When a transversal intersect two PARALLEL lines, then corresponding angles are congruent in other words they have the same angle measure The two small red arrows indicate the two lines are parallel

13 42 When a transversal intersect two PARALLEL lines the alternate interior angles are congruent In this example < 1 and < 2 <3 and < 4

13 42 When a transversal intersects two PARALLEL lines, then the same-side interior angles are supplementary This is saying m < 1 + m < 4 = 180 Likewise m < 2 + m < 3 = 180

What are some things we can state from this diagram? Parallel lines Alternate interior angles Corresponding angles Same side interior angles Vertical angles l m t If <6 and < 2 are corresponding then <1 and <6 are vertical so <1 and < 2 would also have the same measure

a b cd 50 0 Find the measure of each angle:

xy Find the values of x and y x = Corresponding angles of parallel lines are congruent y = y = 180

2x y (y – 50 0 ) Find the values of x and y. Then find the measure of the angles Same side interior angles = x = 180 x = 45 y + y – 50 = 180 2y – 50 = 180 2y = 230 y =

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