Slope and the coordinate formulas are the tools. The unit is about knowing each quadrilateral's properties, using them to solve for missing pieces, and proving what a shape is from its coordinates.
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Opposite sides ≅ / ∥Opposite angles ≅Consecutive angles supp.Diagonals bisect each otherRectangle: diagonals ≅Rhombus: diagonals ⊥Kite: consecutive sides ≅Iso. trapezoid: legs ≅, diagonals ≅∥ = same slope⊥ = negative reciprocal slopesMidpoint formulaDistance formula
Before you answer
✓Sketch the points first. The picture tells you what to guess.
✓Parallelogram? Check the diagonals' midpoints. Same midpoint = parallelogram.
✓Then the diagonals: ≅ → rectangle, ⊥ → rhombus, both → square.
✓Not a parallelogram? One pair of ∥ sides → trapezoid; 2 pairs of consecutive ≅ sides → kite.
✓Algebra question: are the marked parts opposite, consecutive, or diagonal pieces? That decides the equation.
✓Solved for x? Plug it back in if they asked for a side or angle. Use ± when you square-root.