Geometry Bellwork 9/16/14
Lines that do not intersect and are coplanar. Lines m and n. Section 3.1 Identify Pairs of Lines and Angles Key Concepts: Diagram Parallel lines: Skew lines: Parallel planes: Lines that do not intersect and are coplanar. Lines m and n. Lines that do not intersect and are NOT coplanar. Lines m and k. 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
parallel perpendicular oblique Section 3.1 Identify Pairs of Lines and Angles PARALLEL AND PERPENDICULAR LINES Two lines that are in the same plane are either __________( ), ___________________ ( ), or ___________. parallel perpendicular oblique parallel perpendicular oblique intersect at 90° do not intersect intersect NOT at 90°
Identify Pairs of Lines and Angles Postulates: Section 3.1 Identify Pairs of Lines and Angles Postulates: Postulate 13: Parallel Postulate 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 parallel to the given line. There is exactly one line through P parallel to l. 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. Name a pair of parallel lines. a. MK LS Name a pair of perpendicular lines. b. NP PQ Is PR LS ? Explain. c. No, no parallel markings on . PR
parallel GUIDED PRACTICE for Examples 1 and 2 1. Lines in the same plane that do not intersect are called________________. 2. Lines not in the same plane that do not intersect are called________________. parallel skew
Section 3.1 Identify Pairs of Lines and Angles ANGLES AND TRANVERSALS A _____________ is a _______ that intersects two or more coplanar lines at different __________. Transversals form special angle _________. Name the transversals in each diagram. transversal line points pairs line a line t line b
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.
Identify angle relationships 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 2, 6 3, 7 4, 8 b. Alternate interior Alternate sides, between two lines 2, 7 4, 5 c. Alternate exterior Consecutive interior d. Alternate sides, outside two lines Same side, between two lines 1, 8 3, 6 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