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Understanding Parallel Lines, Skew Lines, and Transversals in Geometry

This section covers essential definitions and concepts related to parallel lines, skew lines, and transversals. Parallel lines are coplanar lines that do not intersect, while skew lines are non-coplanar lines that never intersect. Additionally, the concept of parallel planes is introduced, highlighting pairs of planes that also do not intersect. The description of transversals, which are lines that intersect two or more coplanar lines, is discussed along with the characteristics of various angles formed, including interior, exterior, alternate interior, alternate exterior, consecutive interior, and corresponding angles.

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Understanding Parallel Lines, Skew Lines, and Transversals in Geometry

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  1. 3.1: Parallel lines and Transversals p. 124-129

  2. Definitions • Parallel lines (ll) – lines that are coplanar & do not intersect lll m • Skew lines – lines that are not coplanar & NEVER intersect. • Parallel planes – 2 planes that do not intersect. Example: the floor & the ceiling l m

  3. 1. Line AB & Line DC are _______. 2. Line AB & Line EF are _______. 3. Line BC & Line AH are _______. 4. Plane ABC & plane HGF are _______. Parallel parallel skew parallel A B Complete the above statements with either parallel or skew D C H G E F

  4. Transversal • A line that intersects 2 or more coplanar lines at different points. transversal l m

  5. 2 • 3 4 l 5 6 7 8 m Interior <s - <3, <4, <5, <6 (inside l & m) Exterior <s - <1, <2, <7, <8 (outside l & m) Alternate Interior <s - <3 & <6, <4 & <5 (alternate –opposite sides of the transversal) Alternate Exterior <s - <1 & <8, <2 & <7 Consecutive Interior <s - <3 & <5, <4 & <6 (consecutive – same side of transversal) Corresponding <s - <1 & <5, <2 & <6, <3 & <7, <4 & <8 (same location)

  6. Ex. Name the following: Alt. Int- Alt ext- Corresponding- Consecutive int- Vertical- 2 &7 ; 5 &4 3 & 6 ; 1 & 8 1 2 3 5 1 & 5; 2 & 6 ; 4 & 8 ; 3 & 7 4 6 2 & 5 4 & 7 7 8 1 &4; 3 & 2; 5 & 8; 6 & 7

  7. Assignment

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