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Parallel and Perpendicular Lines

Parallel and Perpendicular Lines. Lines & Angles Section 3-1. Lines & Angles. Parallel Lines ( ll ) - are coplanar and do not intersect. Perpendicular Lines (⏊) – intersect at 90 ํ angles . Skew Lines – are not coplanar. Skew lines are not parallel and do not intersect.

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Parallel and Perpendicular Lines

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  1. Parallel and Perpendicular Lines Lines & Angles Section 3-1

  2. Lines & Angles • Parallel Lines (ll) - are coplanar and do not intersect. • Perpendicular Lines (⏊) – intersect at 90ํangles. • Skew Lines – are not coplanar. Skew lines are not parallel and do not intersect. • Parallel Planes – are planes that do not intersect. • **See diagram on pg. 146 for examples**

  3. Examples: What are some examples of perpendicular lines??

  4. Angle Pairs formed by a Transversal • Transversal – a line that intersects two coplanar lines at two different points. The transversal t and the other two lines r and s for eight angles. • Corresponding angles – lie on the same side of the transversal t, on the same sides of lines r and s. (∠1 & ∠5) • Alternate interior angles – nonadjacent angles that lie on opposite sides of the transversal t, between lines r and s. (∠3 & ∠5) • Alternate exterior angles – lie on opposite sides of the transversal t, outside lines r and s.(∠2 & ∠8) • Same-side interior angles – lie on the same side of the transversal t, between lines r and s. (∠3 & ∠6)

  5. Angles formed by parallel lines & transversals Section 3-2

  6. Corresponding Angles Postulate • If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. • Name the pairs of corresponding angles.

  7. Alternate Interior Angles Theorem • If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. • What are the alt. int. angles?

  8. Alternate Exterior Angles Theorem • If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. • Exterior angles (using correct lingo on how to name an angle)??

  9. Same-Side Interior Angles Theorem • If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary. • Example???

  10. Name ‘em: • Alternate Interior Angles: • Alternate Exterior Angles:

  11. Name ‘em: • Corresponding Angles: • Same-side:

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