3. 1 Lines and Angles 3. 3 Parallel Lines and Transversals 3 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. Be able to prove and use results about parallel lines and transversals. Be able to use properties of parallel lines.

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.

Identifying relationships in space Example 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 B C D A F G E H

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

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.

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.

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

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

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

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

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

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.

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

Parallel Lines 3.1 3.3 3.4 3.5 Work Day Pages 132-134 #10-13, 21-31, 41-47 Pages 146-149 #8-26 Pages 153-156 #10-26