3.1 and 3.2 Parallel lines and transversals

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Presentation transcript:

3.1 and 3.2 Parallel lines and transversals Chapter 3 3.1 and 3.2 Parallel lines and transversals

Parallel Lines Parallel lines are coplanar lines that do not intersect. symbol ||

Skew Lines Skew lines are lines that are non-coplanar and do not intersect. Ex: What lines are skew to ?

Parallel Planes Parallel planes are planes that do not intersect. Ex : Name a set of parallel planes.

Example 1 – do not need to copy problem for notes

Transversal Transversal - A line that intersects two or more lines in a plane at different points. t m n

When the transversal intersects two lines, eight angles are formed, which have special names.

Alternate Interior Angles- Nonadjacent interior angles that lie on opposite sides of the transversal.

Alternate Exterior Angles- nonadjacent exterior angles that lie on opposite sides of the transversal. Angles 1 and 7 Angles 2 and 8

Corresponding Angles – lie on the same side of the transversal and in corresponding positions.

Same Side Interior Angles – interior angles that lie on the same side of the transversal.

Take out worksheet pages 59, 63, 67, 87 #1-12, 14,16-24, 27

Additional Problems

3-1 Corresponding angles postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent.  2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

3-2 Same Side Interior Angles Theorem (or Consecutive angles theorem) If two parallel lines are cut by a transversal, then then each pair of same side interior angles is supplementary. m3 +m5 = 180º, m4 +m6 = 180º 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

Lesson 2-4: Angles and Parallel Lines Alternate Angles 3-1 Alternate Interior Angles Thereom: If two parallel lines are cut by a transversal, then each pair of alternate interior angles are Congruent. 3-3 Alternate Exterior Angles: If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are Congruent.  3   6,  4   5  2   7,  1   8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

Worksheet 3-2 1-12, 14, 15, 16

Homework Pg 144-145 11-29, 37-42 Pg 153-154 7-9, 12-20, 22, 23-24

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