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SECTION 3-1 DEFINITIONS: PARALLEL LINES AND ANGLES

SECTION 3-1 DEFINITIONS: PARALLEL LINES AND ANGLES. Parallel Lines. Definition – Coplanar lines that do not intersect. l. Symbol: || Notation: Line l || line m. A. B. C. D. m. Segments and Rays contained in parallel lines are also parallel. A. B. C. D. AB || CD. AB || CD.

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SECTION 3-1 DEFINITIONS: PARALLEL LINES AND ANGLES

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  1. SECTION 3-1 DEFINITIONS: PARALLEL LINES AND ANGLES

  2. Parallel Lines Definition – Coplanar lines that do not intersect l Symbol: || Notation: Line l || line m A B C D m

  3. Segments and Rays contained in parallel lines are also parallel. A B C D AB || CD AB || CD

  4. In the diagram, PQ and RS do not intersect. But they are NOT parallel. Q Since they are parts of lines, they will eventually intersect. P S R

  5. Skew Lines Definition - Non-coplanar lines that do not intersect

  6. AE and CG are not skew, they are parallel. Why?? Plane AEGC can be created, so AE and CG are considered coplanar lines that never intersect.

  7. Parallel Planes Definition – planes that do not intersect Plane AEHD || Plane CFGB

  8. Theorem 3-1: If two parallel planes (A and B) are cut by a third plane (C), then the lines of intersection are parallel. Plane B  Plane C C line l l B Plane A  Plane C m line m A Therefore, line l || line m

  9. Transversal A line that intersects two or more coplanar lines in different points. m l t b a t

  10. Alternate Interior Angles Definition: Two nonadjacent interior angles on opposite sides of the transversal. t Alternate Interior Angles 1 2 b 3 & 6 4 & 5 3 4 5 6 Alternate Exterior Angles a 7 8 1 & 8 2 & 7

  11. Same-side Interior Angles Definition: Two interior angles on the same side of the transversal. a b Same-Side Interior Angles 3 & 4 5 & 6 8 3 4 1 Same-Side Exterior Angles t 7 5 6 2 1 & 8 2 & 7

  12. Corresponding Angles Definition: Two angles in corresponding positions relative to the two lines. t 1 & 5 2 & 6 1 2 b 3 4 3 & 7 4 & 8 5 6 a 7 8

  13. t Identify the types of angles. 1 5 b 2 6 • 1 & 3 • 3 & 6 • 8 & 5 • 2 & 1 • 1 & 8 • 2 & 4 • 5 & 3 • 3 & 7 Corresponding s Alternate Interior s 3 7 a Same-Side Exterior s 4 8 Linear Pair Alternate Exterior s 9) 6 & 7 10) 2 & 5 11) 2 & 3 12) 4 & 5 Corresponding s Same-Side Interior NO RELATIONSHIP Vertical Angles Linear Pair Same-Side Interior Alternate Exterior

  14. 13) 4 & 12 17) 15 & 16 14) 6 & 11 18) 1 & 14 15) 5 & 10 19) 7 & 11 16) 10 & 13 20) 3 & 15 Corresponding s Linear Pair 1 5 2 6 No Relationship Alternate Exterior Angles 3 7 Alternate Interior s Same-Side Interior s 9 13 4 8 10 14 Vertical Angles Same-Side Exterior s 11 15 12 16 Identify the types of angles.

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