Geometry and Measurement — Quadrilaterals

About this lesson

This unit introduces quadrilaterals and their properties. It begins by defining a quadrilateral and proving that the sum of its interior angles is 360°, using the fact that a diagonal divides it into two triangles. The text then presents special quadrilaterals: trapezium (including right and isosceles trapeziums), parallelogram, rectangle, rhombus, and square. For each, it lists defining features and properties, such as opposite sides parallel and equal, opposite angles equal, consecutive angles supplementary, diagonals bisecting each other, and for rectangles, rhombi, and squares, additional properties like equal diagonals, perpendicular diagonals, and bisecting of angles. The unit also includes a quadrilateral family tree showing relationships among these shapes, and conditions for when a parallelogram becomes a rectangle, rhombus, or square. Worked examples and self-evaluation exercises ask students to find unknown angle measures or side lengths using these properties, and to prove that a given quadrilateral is a parallelogram or a rectangle. Real-life contexts include building designs, a decorative tile pattern, and the Great Pyramid of Giza (its base is a square). By the end, students should be able to identify quadrilaterals, compute missing angles or lengths, and justify classifications.