Parallel Lines and Transversals Geometry Chapter 3 3

Parallel Lines and Transversals Geometry Chapter 3. 3 NCSCOS: 2. 02

Essential Question: l What are the conclusions you get from intersections of two parallel lines by a transversal?

– Parallel Lines and Transversals Objective: Students will be able to solve for missing angles using the properties of transversals

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Angles and Parallel Lines Activity l l Using a ruler, trace over two of the parallel lines on your index card that are near the middle of the card and about an inch apart. Draw a transversal that makes clearly acute and clearly obtuse angles near the center of the card Label the angles with numbers from 1 to 8 Sketch the parallel lines, transversal, and number labels in your notes. We will use this to record observations.

Angles and Parallel Lines Activity l l Cut the index card carefully along the lines you first drew to make six pieces. Try stacking different numbered angles onto each other and see what you observe. Try placing different numbered angles next to each other and see what you Observe Mark your observations on the sketch in your notes

Angles and Parallel Lines Activity l Answer the following questions l How many different sizes of angles where formed? l 2 l What special relationships exist between the angles l Congruent and supplementary l Indicate the two different sizes of angles in your sketch.

Angles and Parallel Lines Activity l How can we use the vocabulary learned Friday, to describe these relationships? l IF parallel lines are cut by a transversal, THEN l l corresponding angles are congruent (Postulate in Text) alternate interior angles are congruent (Theorem in Text) alternate exterior angles are congruent (Theorem in Text) Consecutive Interior angles are Supplementary (Theorem in Text)

Perpendicular Transversal l l l In your notes, trace over two of the parallel lines about one inch apart. Using a protractor, draw a line perpendicular to one of the parallel lines. Extend this perpendicular so that it crosses the other parallel line. Based on your observations in the previous exercise, what should be true about the new angles formed? Verify this with your protractor. If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. (Theorem in Text)

Postulate 15: Corresponding Angles If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Alternate interior Angles Theorem 3. 4 If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Same-Side Interior Angles Theorem 3. 5 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Measure of <7 plus measure of <8 equals 180 degrees.

Alternate Exterior Angles Theorem 3. 6 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Perpendicular Transversal Theorem 3. 7 l If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Frayer Model Alternate Exterior Angles Corresponding Angles Alternate Interior Angles Consecutive Interior Angles