Classify quadrilaterals

Learning Objectives Define and identify the key properties of parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. Explain the hierarchical relationships between different types of quadrilaterals (e.g., a square is a rectangle). Use the distance formula to determine the lengths of sides and diagonals of a quadrilateral on a coordinate plane. Use the slope formula to determine if opposite sides are parallel or if adjacent sides are perpendicular. Use the midpoint formula to determine if the diagonals of a quadrilateral bisect each other. Synthesize information from coordinate formulas to definitively classify a quadrilateral. Justify the classification of a quadrilateral using its calculated geometric properties. Have you ever noticed that the windows on a...

TermDefinitionExample ParallelogramA quadrilateral with two pairs of parallel opposite sides. Key properties: opposite sides are congruent, opposite angles are congruent, and diagonals bisect each other.A standard playing card or a slanted window pane. RectangleA parallelogram with four right angles. Key properties: all properties of a parallelogram plus congruent diagonals.A smartphone screen, a door, or a sheet of paper. RhombusA parallelogram with four congruent sides. Key properties: all properties of a parallelogram plus perpendicular diagonals and diagonals that bisect the angles.The shape of a diamond in a deck of cards or a classic kite shape. SquareA parallelogram that is both a rectangle and a rhombus. It has four congruent sides and four right angles.A chessboard square or a sl...

Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Use this to calculate the length of each side and each diagonal. Comparing these lengths helps identify rhombuses (all sides equal), rectangles (diagonals equal), and squares (both). Slope Formula m = \frac{y_2 - y_1}{x_2 - x_1} Use this to determine if sides are parallel or perpendicular. Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals (e.g., 2/3 and -3/2). Midpoint Formula M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) Use this to find the midpoint of each diagonal. If both diagonals have the same midpoint, they bisect each other, which is a key property of all parallelograms.