Warm-Up 1.Using the lines on a piece of paper as a guide, draw a pair of parallel lines. Now draw a transversal that intersects the parallel lines. Label the angles with numbers.

2.Place a patty paper over the set of angles <1, <2, <3, and <4 and copy the two intersecting lines onto the patty paper. 3.Slide the patty paper down and compare angles 1 through 4 with angles 5 through 8. Warm-Up

2.Place a patty paper over the set of angles <1, <2, <3, and <4 and copy the two intersecting lines onto the patty paper. 3.Slide the patty paper down and compare angles 1 through 4 with angles 5 through 8. Warm-Up

Warm-Up Do you notice a relationship between pairs of corresponding, alternate interior, and alternate exterior angles? What kind of transformation is this?

3.2 Use Parallel Lines and Transversals Objectives: 1.To find angle pair measurements with parallel lines cut by a transversal 2.To prove theorems involving parallel lines cut by a transversal

Transversal transversal A line is a transversal if and only if it intersects two or more coplanar lines. –When a transversal cuts two coplanar lines, it creates 8 angles, pairs of which have special names

Transversal corresponding angles<1 and <5 are corresponding angles alternate interior angles<3 and <6 are alternate interior angles alternate exterior angles<1 and <8 are alternate exterior angles consecutive interior angles<3 and <5 are consecutive interior angles

Four Window Foldable Start by folding a blank piece of paper in half lengthwise, and then folding it in half in the opposite direction. Now fold it in half one more time in the same direction.

Four Window Foldable Now unfold the paper, and then while holding the paper vertically, fold down the top one-fourth to meet the middle. Do the same with the bottom one- fourth.

Four Window Foldable To finish your foldable, cut the two vertical fold lines to create four windows. Outside: Outside: Name Inside Flap: Inside Flap: Illustration Inside: Inside: Postulate or Theorem

Four Window Foldable Corresponding Angles Postulate If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent.

Four Window Foldable Corresponding Angles Postulate If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent.

Parallel Line Theorems Alternate Exterior Angle Theorem If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary.

Example 1 On the map below, 1 st and 2 nd Ave. are parallel.

Example 1 A city planner proposes to locate a small park on the triangular island formed by the intersections of the four streets below.

Example 1 What are the measures of the three angles of the garden? Answer in your notebook

Example 2: SAT In the figure, if l || m, what is the value of x ? HINT: Find y 1 st since there are 2 parts with y. y=25 x=10

Example 3: SAT In the figure, if l 1 || l 2 and l 3 || l 4, what is y in terms of x. y=180-x 2 THINK about it before you look at the answer and TRY!

Example 4 Prove the Alternate Interior Angle Theorem. Given: Prove: TRY IT!!!

Example 5 Given: and Prove: You can EASILY do THIS one!

Example 6 Calculate each lettered angle measure.

Example 7 Find the values of x and y if k || l || m. Did you try it??!?! x=13.8 y=11.2

Assignment P : 2, 3-21 M3, 23, even, 36, 37, 41, Challenge Problems Bring Compass