A line and a plane that do not intersect are parallel. Segments and rays can also be parallel or skew. They are parallel if they lie in parallel lines and skew if they lie in skew lines.
Problem 1 Identifying Nonintersecting Lines and Planes
In the figure, assume that lines and planes that appear to be parallel are parallel.
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Which segments are parallel to
Think
Parallel lines are coplanar. Which planes contain
Planes ABCD, ABFE, and ABGH contain
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Which segments are skew to
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What are two pairs of parallel planes?
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What are two segments parallel to plane BCGF?
✓ Got It?
- Use the figure in Problem 1.
- Which segments are parallel to
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Reasoning Explain why
- What is another pair of parallel planes?
- What are two segments parallel to plane DCGH?
- Which segments are parallel to
Essential Understanding When a line intersects two or more lines, the angles formed at the intersection points create special angle pairs.
A transversal is a line that intersects two or more coplanar lines at distinct points. The diagram below shows the eight angles formed by a transversal t and two lines l and m.
Notice that angles 3, 4, 5, and 6 lie between l and m. They are interior angles. Angles 1, 2, 7, and 8 lie outside of l and m. They are exterior angles.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs