Lesson 7 of 14, 13 min read
Quadrilaterals
Properties of parallelograms, rectangles, rhombuses, squares, trapezoids and kites, including diagonals and the trapezoid midsegment, with algebra problems.
The quadrilateral family
A quadrilateral has four sides, and its interior angles add up to \(360°\). Some quadrilaterals have extra properties, and they fit inside one another like a family tree: every square is a rectangle, every rectangle is a parallelogram, and so on.
Parallelograms
Each property also works in reverse: a quadrilateral whose diagonals bisect each other, for example, must be a parallelogram.
Rectangles, rhombuses and squares
| Shape | Extra property of the diagonals |
|---|---|
| rectangle | congruent |
| rhombus | perpendicular, and each one bisects a pair of opposite angles |
| square | congruent, perpendicular and angle bisectors |
Trapezoids and kites
A trapezoid with bases \(10\) and \(18\) has a midsegment of \(\frac{10 + 18}{2} = 14\).
The diagonals of a kite are perpendicular, and one of them bisects the other.
Practice
Quick check
Which quadrilateral always has congruent diagonals that aren't necessarily perpendicular?
Rectangle diagonals are always congruent but are perpendicular only when the rectangle is a square.
Quick check
Is every square a rhombus?
A rhombus is any parallelogram with four congruent sides. A square has that property, plus right angles.
Finished this lesson?
Mark it as completed and it's saved on this device. Sign up to see it everywhere.