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Objectives:

3.3 Parallel Lines & Transversals. Objectives: -Define transversal, alternate interior, alternate exterior, same side interior, and corresponding angles -Make conjectures and prove theorems by using postulates and properties of parallel lines and transversals. Warm-Up:

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Objectives:

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  1. 3.3 Parallel Lines & Transversals Objectives: -Define transversal, alternate interior, alternate exterior, same side interior, and corresponding angles -Make conjectures and prove theorems by using postulates and properties of parallel lines and transversals Warm-Up: What weighs more: a pound of feathers or a pound of bricks?

  2. Transversal: a line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.

  3. Interior & Exterior Angles: Exterior Interior Exterior

  4. Alternate Interior Angles: 1 2 3 4 5 6 8 7 Alternate Interior Theorem: If two lines cut by a transversal are parallel then, alternate interior angles are congruent.

  5. Proof: The Alternate Interior Angles Theorem Given: Prove: Statements Reasons

  6. Alternate Exterior Angles: 1 2 3 4 5 6 8 7 Alternate Exterior Angle Theorem: If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.

  7. Proof: The Alternate Exterior Angles Theorem Given: Prove: Statements Reasons

  8. Same Side Interior Angles: 1 2 3 4 5 6 8 7 Same Side Interior Angle Theorem: If two lines cut by a transversal are parallel, then same side interior angles are supplementary.

  9. Proof: The Same Side Interior Angles Theorem Given: Prove: Statements Reasons

  10. Corresponding Angles: 1 2 3 4 5 6 8 7 Corresponding Angles Postulate: If two lines cut by a transversal are parallel, then corresponding angles are congruent.

  11. Example: List all of the angles that are congruent to <1: 1 2 3 4 List all of the angles that are congruent to <2: 5 6 8 7 Identify each of the following: alternate interior angles: alternate exterior angles: same side interior angles: corresponding angles:

  12. Example: 1 2 3 4 5 6 8 7 If m<1 = find the measurements of each of the remaining angles in the figure. m<2 = m<3 = m<6 = m<7= m<4 = m<5 = m<8 =

  13. Example: 1 2 3 4 If m<3 = and m<7 = find the measurements of each of the angles in the figure. 5 6 8 7 m<2 = m<3 = m<6 = m<7 = m<1 = m<4 = m<5 = m<8 =

  14. Example: 1 2 3 4 If m<3 = and m<5 = find the measurements of each of the angles in the figure. 5 6 8 7 m<2 = m<3 = m<6 = m<7 = m<1 = m<4 = m<5 = m<8 =

  15. Example: In triangle KLM, NO is parallel to ML and <KNO is congruent to <KON. Find the indicated measures. m<KNO = m<NOL = m<MNL = m<KON = m<LNO = m<KLN = K O N L M

  16. HOMEWORK: page 159-160 #’s 5-12, 22-33

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