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Objectives: Be able to identify relationships between lines.

3.1 Lines and Angles 3.3 Parallel Lines and Transversals 3.4 Proving Lines Parallel 3.5 Using Properties of Parallel Lines. Objectives: Be able to identify relationships between lines. Be able to identify angles formed by transversals.

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Objectives: Be able to identify relationships between lines.

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  1. 3.1 Lines and Angles3.3 Parallel Lines and Transversals3.4 Proving Lines Parallel3.5 Using Properties of Parallel Lines Objectives: • Be able to identify relationships between lines. • Be able to identify angles formed by transversals. • Be able to prove and use results about parallel lines and transversals. • Be able to use properties of parallel lines.

  2. Definitions • Parallel lines – Two lines are parallel lines if they are coplanar and do not intersect. • Skew lines—Lines that do not intersect and are not coplanar. • Parallel planes—two planes that do not intersect.

  3. 1) Think of each segment in the diagram. Which appear to fit the description? Parallel to AB and contains D Perpendicular to AB and contains D Skew to AB and contains D Name the plane(s) that contains D and appear to be parallel to plane ABE Identifying relationships in space Example B C D A F G E H

  4. Postulate 13: Parallel Postulate • If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. P l

  5. Parallel Construction-Copying an Angle Page 159 Use the following steps to construct an angle that is congruent to a given angle A. • Using a straight edge, draw an angle A. • Using a straight edge, draw a line below angle A. Label a point on the line D. • Draw an arc with center A. Label B and C. With the same radius, draw an arc with center D. Label E. • Draw DF.

  6. Parallel Construction-Parallel Lines Page 159 Use the following steps to construct a line that passes through a given point P and is parallel to a given line m. • Using a straight edge, draw line m. • Draw points Q and R on line m. • Draw PQ. • Draw an arc with a compass point at Q so that it crosses QP and QR. • Copy angle PQR on QP. Be sure the two angles are corresponding. Label the new angle TPS. • Draw PS.

  7. Identifying Angles Formed by Transversals Exterior Angles Interior Angles Consecutive Interior Angles or Same Side Interior 1 2 3 4 Alternate Exterior Angles 6 5 8 7 Alternate Interior Angles Corresponding Angles

  8. Corresponding Angles Postulate 15 Postulate 16 Corresponding Angle Converse If 2  lines are cut by a transversal, then the pairs of corresponding s are . 1 l m 2

  9. Alternate Interior Angles Theorem 3.4 Theorem 3.8 Alternate Interior Angle Converse If 2  lines are cut by a transversal, then the pairs of alternate interior s are . l m 1 2

  10. Consecutive Interior Angles Theorem 3.5 Theorem 3.9 Consecutive Interior Angle Converse If 2  lines are cut by a transversal, then the pairs of consecutive interior s are supplementary. l m 1 2

  11. Alternate Exterior Angles Theorem 3.6 Theorem 3.10 Alternate Exterior Angle Converse If 2  lines are cut by a transversal, then the pairs of alternate interior s are . 1 l m 2

  12. Parallel Lines Theorem • Theorem 3.11: If two lines are parallel to the same line, then they are parallel to each other. r q p If p║q and q║r, then p║r.

  13. ASSIGNMENT • Read 129-131, 143-145, and 150-152 • 3X5 Cards: Parallel Lines, Skew Lines, Parallel Planes, Postulate 15 and 16, Theorems 3.4, 3.5, 3.6, 3.8, 3.9, 3.10. 3.11

  14. Work Day Parallel Lines 3.13.33.43.5 • Pages 132-134 #10-13, 21-31, 41-47 • Pages 146-149 #8-26 • Pages 153-156 #10-26

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