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The concepts of parallel lines, skew lines, and perpendicular lines, as well as parallel planes. It includes definitions, examples, and illustrations. The document also discusses the Parallel and Perpendicular Postulate and its implications for identifying parallel and perpendicular lines and planes.
Typology: Exercises
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Skew, Parallel Lines, Planes, Perpendicular d. (^) Plane ( s ) parallel to plane EFG and containing point A c. Line ( s )^ perpendicular to^ CD^ and containing point^ A a. Line ( s ) parallel to CD and containing point A b. Line ( s ) skew to CD and containing point A 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? AB , HG , and EF all appear parallel to CD , but only AB contains point A. Both AG and AH is skew to CD and contain point A. BC , AD , DE , and FC all appear perpendicular to CD , but only AD contains point A. Plane ABC appears parallel to plane EFG and contains point A.
Skew, Parallel Lines, Planes, Perpendicular
1. (^) Look at the diagram in Example 1. Name the lines through point H that appear skew to CD. ANSWER AH , EH
l 1 l 2 l 3 l 1 l 2 l 3
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Angles Formed by Transversal Line
1 2 3 4 (^5 ) (^7 )
CORRESPONDING ANGLES: ALTERNATE EXTERIOR ANGLES: SAME SIDE/ CONSECUTIVE INTERIOR ANGLES: ALTERNATE INTERIOR ANGLES: ๏1 and ๏5, ๏1 and ๏8, ๏3 and ๏6, ๏3 and ๏5, ๏2 and ๏6, ๏3 and ๏7, ๏4 and^ ๏^8 ๏2 and ๏ 7 ๏4 and ๏ 5 ๏4 and ๏ 6
3. (^) 4. 5. Corresponding angles Alternate exterior angles Alternate interior angles
1. ) If m ๏ 1 = 125^0 , find m ๏ 2 =_____ 2. ) If m ๏ 8 =135^0 , find m ๏ 2 =_____ 3. ) If m ๏ 5 = 87 0 , find m ๏ **4 =_____
Vertical Angles Congruence Corresponding Angles Alternate Exterior Angles
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