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Parallel Lines and Transversals

This activity helps students understand the properties of angles formed by the intersection of two parallel lines with a transversal. By tracing, cutting, and stacking angles, they explore congruent, supplementary, and perpendicular relationships.

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Parallel Lines and Transversals

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  1. Parallel Lines and Transversals Geometry Chapter 3.3 NCSCOS: 2.02

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

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

  4. Angles and Parallel Lines Activity • 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.

  5. Angles and Parallel Lines Activity • 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

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

  7. Angles and Parallel Lines Activity • How can we use the vocabulary learned Friday, to describe these relationships? • IF parallel lines are cut by a transversal, THEN • 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)

  8. Perpendicular Transversal • 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)

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

  10. Alternate interior Angles Theorem 3.4 If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

  11. Same-Side Interior AnglesTheorem 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.

  12. Alternate Exterior AnglesTheorem 3.6 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

  13. Perpendicular TransversalTheorem 3.7 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

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

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