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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

Parallel and Perpendicular Lines

Lines & Angles

Section 3-1


Lines angles
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**


Examples
Examples:

What are some examples of perpendicular lines??


Angle pairs formed by a transversal
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)



Corresponding angles postulate
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.


Alternate interior angles theorem
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?


Alternate exterior angles theorem
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)??


Same side interior angles theorem
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???


Name em
Name ‘em:

  • Alternate Interior Angles:

  • Alternate Exterior Angles:


Name em1
Name ‘em:

  • Corresponding Angles:

  • Same-side:


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