Parallelograms

Geometry · Axiom Academy

Properties of quadrilaterals with two pairs of parallel sides A parallelogram is a quadrilateral with two pairs of parallel sides. Label the vertices A, B, C, D in order: then the opposite sides run parallel, and the two diagonals cross at a single point M that splits each one exactly in half. 2. Properties of Parallelograms The parallel-sides condition forces six properties. The animation lights up the matching opposite pairs — sides, then angles — so you can see why each comes in twos. Slide the slanted top of the parallelogram straight across until it becomes a rectangle. Nothing is added or removed — so the area is base × height , where the height is measured perpendicular to the base, not along the slanted side. The height h is the perpendicular distance between the parallel bases — shorter than the slanted side unless the shape is a rectangle. Cutting the triangle off one end and sliding it to the other turns the parallelogram into a rectangle of the same base and height. 4. Worked Example: Chasing the Angles Watch the known angle at A propagate around the parallelogram: its opposite angle copies it, and each neighbor fills the gap up to 180°. In parallelogram ABCD , . Find , , and . You've seen how one rule — two pairs of parallel sides — forces a parallelogram's equal sides, equal angles, and bisecting diagonals, and how to use them. Scroll up to revisit any step.

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