Example 5

A square is a quadrilateral with two pairs of parallel opposite sides, consecutive sides that are perpendicular, and all sides congruent, meaning they have the same length. Quadrilateral ABCD has vertices A (–1, 2), B (1, 5), C (4, 3), and D (2, 0). Determine if this quadrilateral is a square. Note: Drag the blue points to try different figures.
  1. Plot the quadrilateral on a coordinate plane.
  2. First show the figure has two pairs of parallel opposite sides. Calculate the slope of each side using the general slope formula.
  3. Observe the slopes of each side.
  4. Show that the quadrilateral has four congruent sides.
  5. Make connections.
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