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Objectives: Develop & use theorems about equal slopes & slopes of perpendicular lines.

3.8 Analyzing Polygons with Coordinates. Objectives: Develop & use theorems about equal slopes & slopes of perpendicular lines. Solve problems involving perpendicular and parallel lines in the coordinate plane by using appropriate theorems. Warm-Up:.

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Objectives: Develop & use theorems about equal slopes & slopes of perpendicular lines.

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  1. 3.8 Analyzing Polygons with Coordinates Objectives: Develop & use theorems about equal slopes & slopes of perpendicular lines. Solve problems involving perpendicular and parallel lines in the coordinate plane by using appropriate theorems Warm-Up: As illustrated, at present this carton holds exactly one dozen eggs. How is it possible to position thirteen eggs in the same carton without breaking or scrambling a single egg? Placing two eggs in any single compartment is not allowed.

  2. Slope: the slope of a nonvertical line that contains the points &is equal to the ratio:

  3. Find the slope of the segment AB • with endpoints A=(5,3) & B=(2,3) • Find the slope of the segment AB • with endpoints A=(-2,5) & B=(4,8)

  4. Graph:

  5. Parallel Lines Theorem: In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Note: Any two vertical lines are parallel

  6. Graph:

  7. Perpendicular Lines Theorem: In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1 (opposite reciprocals). Note: Any vertical line is perpendicular to any horizontal line.

  8. The endpoints of two segments are given. • Determine whether the segments are parallel, perpendicular, or neither. • Segment 1: (-2,1) & (1,-2) • Segment 2: (-1,-1) & (3,3)

  9. The endpoints of two segments are given. • Determine whether the segments are parallel, perpendicular, or neither. • Segment 1: (-1,2) & (1,-2) • Segment 2: (1,-2) & (2,-1)

  10. Graph quadrilateral QUAD with vertices Q(1,4), U(7,8), A(9,5), D(3,1) • What type of quadrilateral is it? (compare the slopes of the sides)

  11. Midpoint Formula: The midpoint of a segment with endpoints andhas the following coordinates: ,

  12. The endpoints of two segments are given. • Find the slope and the midpoint of the segment. • (-1,1) & (1,-1)

  13. The endpoints of two segments are given. • Find the slope and the midpoint of the segment. • (-5,2) & (1,-3)

  14. The vertices of a triangle are given. • Use the slopes to determine whether each triangle is a right triangle. • (9,5) (2,-6) (-1,-1)

  15. The vertices of a triangle are given. • Use the slopes to determine whether each triangle is a right triangle. • (1,2) (3,3) (4,0)

  16. Homework: • Page 194 – • Numbers 12, 14, 16, 18-24

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