The parallelogram, rectangle, rhombus and square
Learn the elements of a quadrilateral, the properties and criteria of a parallelogram, and the diagonals of a rectangle and a rhombus, as in the Grade 8 Ukrainian geometry book.
- Germany: grade 7
- Ukraine: grade 8
Guide
In the Ukrainian programme quadrilaterals are Grade 8 geometry, §1, items 1-6: the quadrilateral and its elements, the parallelogram, its criteria, the rectangle, the rhombus and the square.
In quadrilateral ABCD the vertices A and C (and B and D) are opposite, AC and BD are diagonals, and AB and CD (and BC and AD) are opposite sides. The angles add up to 360°. The perimeter is P = AB + BC + CD + DA.
A parallelogram has both pairs of opposite sides parallel. Its opposite sides are equal, its opposite angles are equal and its diagonals bisect each other. Criteria: both pairs of opposite sides equal; two opposite sides equal and parallel; diagonals that bisect each other.
A rectangle is a parallelogram with a right angle; its diagonals are equal. A rhombus is a parallelogram with equal sides: its diagonals are perpendicular and bisect the angles. A square is both a rectangle and a rhombus.