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