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3.1 Identify Pairs of Lines and Angles

3.1 Identify Pairs of Lines and Angles. Objectives. Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal. Relationships Between Lines.

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3.1 Identify Pairs of Lines and Angles

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  1. 3.1 Identify Pairs of Lines and Angles

  2. Objectives • Identify the relationships between two lines or two planes • Name angles formed by a pair of lines and a transversal

  3. Relationships Between Lines • Parallel Lines– lines that are coplanar and do not intersect; We use the symbol ||to represent parallel lines, (i.e. AB || CD). • Skew Lines– lines that do not intersect and are not coplanar • Parallel Planes– two planes that do not intersect

  4. EXAMPLE 1 Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? a. Line(s) parallel to CDand containing point A b. Line(s) skew to CDand containing point A Line(s) perpendicular to CDand containing point A c. d. Plane(s) parallel to plane EFGand containing point A EXAMPLE 1 Identify Relationships in Space

  5. EXAMPLE 1 (solution) AB, HG, and EFall appear parallel to CD, but only ABcontains point A. a. b. Both AGand AHappear skew to CDand contain point A. BC, AD, DE, and FCall appear perpendicular to CD, but only ADcontains pointA. c. PlaneABCappears parallel to plane EFGand contains point A. d. Identify Relationships in Space

  6. EXAMPLE 2 The given line markings show how the roads are related to one another. a. Name a pair of parallel lines. b. Name a pair of perpendicular lines. Is FEAC? Explain. c. EXAMPLE 2 Identify Parallel and Perpendicular Lines

  7. b. MDBF c. FEis not parallel to AC, because MDis parallel to FEand by the Parallel Postulate there is exactly one line parallel to FEthrough M. EXAMPLE 2 (solution) a. MDFE EXAMPLE 2 Identify Parallel and Perpendicular Lines

  8. 1. Look at the diagram in Example 1. Name the lines through point Hthat appear skew to CD. ANSWER AH , EH YOUR TURN GUIDED PRACTICE

  9. ANSWER Yes; Since A is not on MD and MD is to BF, the Perpendicular Postulate guarantees that there is exactly one line through a point perpendicular to a line, so AC can not be perpendicular to BF also. YOUR TURN GUIDED PRACTICE 2. In Example 2, can you use the Perpendicular Postulate to show that ACis not perpendicular to BF? Explain why or why not.

  10. Postulates • Postulate 13 (Parallel Postulate)– There is exactly one line through a point that is parallel to a given line. • Postulate 14 (Perpendicular Postulate) – There is exactly one line through a point that is perpendicular to a given line.

  11. 1 2 3 4 5 6 7 8 Relationships Between Lines and the Angles Formed • Transversal- a line that intersects two or more coplanar lines at different points • Angles 1 and 5 are corresponding angles • Angles 1 and 8 are alternate exterior angles

  12. 1 2 3 4 5 6 7 8 Relationships Between Lines and the Angles Formed • Angles 3 and 6 are alternate interior angles. • Angles 3 and 5 are consecutive interior angles orsame side interior angles

  13. EXAMPLE 3 Identify all pairs of angles of the given type. d. b. a. Corresponding Alternate interior d. Consecutive interior Alternate exterior c. and and and and and and and and and and ∠ 5 ∠ 6 ∠ 7 ∠ 5 ∠ 6 ∠ 7 ∠ 7 ∠ 8 ∠ 8 ∠ 5 1 4 2 2 4 3 3 2 4 1 a. b. c. EXAMPLE 3 Identify Angle Relationships SOLUTION

  14. YOUR TURN 1. ANSWER corresponding angles GUIDED PRACTICE Classify the pair of numbered angles.

  15. YOUR TURN 2. ANSWER alternate exterior angles. GUIDED PRACTICE Classify the pair of numbered angles.

  16. Assignment • Geometry: Pg. 150 – 152 #3 – 33, 36

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