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Understanding Slope and Rate of Change in Geometry

This lesson focuses on the concept of slope as the rate of change in geometry, identifying whether slopes are positive, negative, zero, or undefined. We'll explore important postulates: two distinct nonvertical lines are parallel if they have the same slope, and they are perpendicular if the product of their slopes equals -1, indicating they are negative reciprocals. Examples include finding slopes between pairs of points and determining relationships between line segments. Homework is assigned for practice.

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Understanding Slope and Rate of Change in Geometry

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  1. Geometry 3.3 Slope

  2. Slope- rate of change • m = • PositiveNegativeZeroUndefined

  3. Example1 • Find the slope between each pair of points. A. (0, 2) and (2, 0) B. (5, 2) and (-6, -1) C. (-3, -2) and (2, -2) D. (5, 2) and (5, -3)

  4. Postulate 3-2: Two distinct nonvertical lines are parallel if and only if they have the same slope. • Postulate 3-3: Two nonvertical lines are perpendicular if and only if the product of their slopes is -1 • This also means that they are negative reciprocals.

  5. Example 2 • Given F(1, -3), G(-2, -1), H(5, 0), and J(6,3) determine if FG and HJ are parallel, perpendicular, or neither.

  6. Homework • Page 190: 13 – 37 odds

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