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Section 14.3: Proving Lines are Parallel

Learn to prove lines are parallel using corresponding, alternate interior, and same-side interior angles. Apply angle values in mosaic designs to show line parallelism. Construct parallel lines with a compass and straight edge. Identify angle pairs and reasons for parallel lines.

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Section 14.3: Proving Lines are Parallel

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  1. Section 14.3: Proving Lines are Parallel

  2. Objective: By following instructions, students will be able to: • Prove that two lines are parallel.

  3. Corresponding Angles Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. If (pair of corresponding angles that are congruent), then p // q.

  4. Alternate Interior Angles Converse If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. If (pair of alternate interior angles that are congruent), then p // q.

  5. Same-Side Interior Angles Converse

  6. explain 1A A mosaic designer is using quadrilateral-shaped colored tiles to make an ornamental design. Each tile is congruent to the one shown here. The designer uses the colored tiles to create the pattern shown. Use the values of the marked angles to show that line 1 and line 2 are parallel.

  7. explain 1B A mosaic designer is using quadrilateral-shaped colored tiles to make an ornamental design. Each tile is congruent to the one shown here. Now look at this situation. Use the values of the marked angles to show that the two lines are parallel.

  8. Your-Turn #1 Explain why the lines are parallel given the angles shown. Assume that all tile patterns use this basic shape.

  9. explain 2A • Use a compass and straight edge to construct parallel lines. Construct a line m through a point P not on a line l so that m is parallel to l.

  10. explain 2B • Use a compass and straight edge to construct parallel lines. Construct a line r through a point G not on a line s so that r is parallel to s.

  11. Your-Turn #2 Construct a line m through P parallel to line ℓ.

  12. explain 3A • Use the given angle relationships to decide whether the lines are parallel. Explain your reasoning. ∠3 ≅ ∠5

  13. explain 3B • Use the given angle relationships to decide whether the lines are parallel. Explain your reasoning. m∠4 = (x + 20) °, m∠8 = (2x + 5) °, and x = 15.

  14. Your-Turn #3 Identify the type of angle pair described in the given condition. How do you know that lines and m are parallel? m∠3 + m∠6 = 180°

  15. Revisit Objective: Did we… • Prove that two lines are parallel?

  16. HW: • Sec 14.3 pg 524 #s 1-12

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