Geometry Bellwork 9/16/14 Section 3.1 Identify Pairs of Lines and Angles Key Concepts: Diagram Parallel lines: Lines that do not intersect and are coplanar. Lines m and n. Skew lines: Lines that do not intersect and are NOT coplanar. Lines m and k. Parallel planes: Planes that do not intersect. Planes T and U. EXAMPLE 1 Identify relationships in space Think of each segment in the figure as part of a line. Complete the statements. a. Name the 3 lines parallel to CD . AB , HG, EF b. Name the 4 lines perpendicular to AH . HG , EH , AB, DA c. Name the 5 lines skew to ED. HG, FG, AB, CB, AG d. Is plane EFG parallel, skew, or perpendicular to plane CFG? perpendicular Section 3.1 Identify Pairs of Lines and Angles PARALLEL AND PERPENDICULAR LINES Two lines that are in the same plane are either __________( parallel perpendicular ___________________ ( parallel do not intersect ), oblique ), or ___________. perpendicular intersect at 90° oblique intersect NOT at 90° Section 3.1 Identify Pairs of Lines and Angles Postulates: 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. There is exactly one line through P parallel to l. Postulate 14: Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. There is exactly one line through P perpendicular to l. EXAMPLE 2 Identify parallel and perpendicular lines Use the markings in the diagram. a. Name a pair of parallel lines. MK LS b. Name a pair of perpendicular lines. NP c. Is PR PQ LS ? Explain. No, no parallel markings on PR . GUIDED PRACTICE for Examples 1 and 2 1. Lines in the same plane that do not intersect are parallel called________________. 2. Lines not in the same plane that do not intersect skew are called________________. Section 3.1 Identify Pairs of Lines and Angles ANGLES AND TRANVERSALS transversal is a A _____________ line that intersects two or more coplanar lines at _______ points different __________. Transversals form special angle pairs _________. Name the transversals in each diagram. line t line b line a Section 3.1 Identify Pairs of Lines and Angles Key Concepts: Angles formed by transversals Corresponding angles: Two angles that have corresponding positions on the same side of a transversal. Section 3.1 Identify Pairs of Lines and Angles Key Concepts: Angles formed by transversals Consecutive interior angles: Two angles that lie between the two lines on the same side of a transversal. Section 3.1 Identify Pairs of Lines and Angles Key Concepts: Angles formed by transversals Alternate interior angles: Two angles that lie between the two lines on opposite sides of a transversal. Section 3.1 Identify Pairs of Lines and Angles Key Concepts: Angles formed by transversals Alternate exterior angles: Two angles that lie outside the two lines on opposite sides of a transversal. EXAMPLE 3 Identify angle relationships Identify all pairs of angles of the given type. Transversal connects angle pairs a. Corresponding Same side transversal, corresponding spots 1, 5 3, 7 2, 6 4, 8 b. Alternate interior Alternate sides, between two lines 2, 7 4, 5 c. Alternate exterior Alternate sides, outside two lines 1, 8 3, 6 d. Consecutive interior Same side, between two lines 2, 5 4, 7 GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 3. Corresponding (CORR) GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 4. Alternate Exterior (AE) GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 5. Alternate Interior (AI) HOMEWORK Worksheet 3.1 Worksheet 3.1 Skip #’s 25 to 30

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