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4-2: Parallel Lines and Transversals

Learn about the angles formed by parallel lines and transversals, including alternate interior, alternate exterior, consecutive interior, and vertical angles. Explore the theorems that govern these angle relationships. Solve angle measurement problems with a given angle. Complete a worksheet.

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4-2: Parallel Lines and Transversals

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  1. 4-2: Parallel Lines and Transversals

  2. 4-2: Parallel Lines and Transversals • Transversal: A line, line segment, or ray that intersects two or more lines at different points.

  3. 4-2: Parallel Lines and Transversals • When a transversal intersects two lines, eight angles are formed. • Interior Angles: Angles between the two lines • 3, 4, 5, 6 • Alternate Interior Angles:pairs of interior angles that are on opposite sides of the transversal • 3 & 5, 4 & 6 • Consecutive Interior Angles: pairs of interior angles that are on the same side of the transversal • 4 & 5, 3 & 6 • Exterior Angles: Angles that lie outside the two lines • 1, 2, 7, 8 • Alternate exterior Angles: pairs of exterior angles that are on opposite sides of the transversal • 1 & 7, 2 & 8

  4. 4-2: Parallel Lines and Transversals • Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical • 2 & 8 • 1 & 6 • 2 & 4 • 4 & 6 Alternate exterior Consecutive interior Vertical Alternate interior

  5. 4-2: Parallel Lines and Transversals • If two parallel lines are cut by a transversal, then… • THEOREM 4-1: alternate interior angles are congruent (3  5, 4  6) • THEOREM 4-2: consecutive interior angles are supplementary (3 + 6 = 180˚, 4 + 5 = 180˚) • THEOREM 4-3: alternate exterior angles are congruent (1  7, 2  8)

  6. 4-2: Parallel Lines and Transversals • In the figure, p || q, andr is a transversal. If m5 = 28, find: • m8 • m1 • m2 • m3 • m4 28 152 28 28 152

  7. 4-2: Parallel Lines and Transversals • Assignment • Worksheet #4-2

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