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Parallelograms, trapezoids & rhombuses

Basic shapes

Japanese school year: Elementary 4

What you learn

Learn the geometric properties of trapezoids, parallelograms, and rhombuses by examining parallel sides, side lengths, and diagonals. These quadrilaterals are used in creating tessellation patterns and analyzing mechanical linkages. Prior understanding of parallel and perpendicular lines, as well as angle measurement, will make classifying and constructing them straightforward.

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Key points

This formula shows the side property of a parallelogram. Opposite sides (AB and CD, AD and BC) have equal lengths.

AB=CD,AD=BCAB = CD, \quad AD = BC

This formula shows the angle property of a parallelogram. Opposite angles (angle A and C, angle B and D) are equal.

∠A=∠C,∠B=∠D\angle A = \angle C, \quad \angle B = \angle D

This equation defines a rhombus. A four-sided shape where all sides AB, BC, CD, and DA have equal length is a rhombus.

AB=BC=CD=DAAB = BC = CD = DA

This formula shows the diagonal property of a rhombus. The two diagonals AC and BD cross each other at a right angle (90°).

AC⊥BDAC \perp BD

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