Quadrilaterals
Grades 6–8 Geometry Polygons
Four sides, 360° inside. Every quadrilateral splits into two triangles along a diagonal — which is why its angles sum to 2 × 180° = 360°.
The family tree
- Parallelogram — both pairs of opposite sides parallel; opposite sides and angles equal
- Rectangle — a parallelogram with four 90° corners
- Rhombus — a parallelogram with four equal sides
- Square — both: equal sides and right angles
- Trapezoid — just one pair of parallel sides
A square is a rectangle, a rhombus, and a parallelogram — the most decorated member of the family.
Finding missing angles
Parallelogram with angles 110°, 110°, and ?:
360 − 110 − 110 = 140 → split: 70° and 70°
(opposite angles in a parallelogram are equal)
The diagonal trick
Diagonals of a parallelogram bisect each other — they cut each
other exactly in half. In a rectangle they're also equal; in a
rhombus they cross at 90°.
Practice
The angles of any quadrilateral sum to ___°
A rhombus with one 90° angle must be a:
Three angles are 90°, 100°, and 90°. The fourth is ___°
Which has exactly one pair of parallel sides?