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Geometry Relationships and Angle Classifications

Identify relationships between lines and angles in space, classify angle pairs, and determine parallel, perpendicular, or skew relationships.

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Geometry Relationships and Angle Classifications

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  1. 1.Name a line that does not intersect AD. BC ANSWER 2.What is the intersection of AD and DB? D ANSWER

  2. 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

  3. 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. EXAMPLE 1 Identify relationships in space SOLUTION

  4. Photography 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

  5. 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. a. MDFE EXAMPLE 2 Identify parallel and perpendicular lines SOLUTION

  6. 1. Look at the diagram in Example 1. Name the lines through point Hthat appear skew to CD. ANSWER AH , EH for Examples 1 and 2 GUIDED PRACTICE

  7. 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. for Examples 1 and 2 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.

  8. 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 6 8 7 5 7 8 5 6 7 5 1 2 3 4 2 4 1 2 3 4 a. b. c. EXAMPLE 3 Identify angle relationships SOLUTION

  9. 3. ANSWER corresponding angles for Example 3 GUIDED PRACTICE Classify the pair of numbered angles.

  10. 4. ANSWER alternate exterior angles. for Example 3 GUIDED PRACTICE Classify the pair of numbered angles.

  11. 5. ANSWER alternate interiorangles. for Example 3 GUIDED PRACTICE Classify the pair of numbered angles.

  12. 1. Name the pairs of corresponding angles . 1 and 3; 5 and 7; ANSWER 2 and 4; 6 and 8 2. 3. Name the pairs of alternate interior angles . Name the pairs of consecutive interior angles . 2 and 7; 3 and 6 ANSWER 2 and 3; 6 and 7 ANSWER Daily Homework Quiz

  13. 4. The figure shows a painting easel. Does AB appear to be parallel, perpendicular, or skew to CD? Parallel ANSWER Daily Homework Quiz

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