Quadrilaterals - Mathable Smart Lab

GRADE 8 • GEOMETRY Strand: Quadrilaterals and Deductive Reasoning

Quadrilaterals Smart Lab

Explore rectangles, squares, parallelograms, angle sums, diagonals, Venn relations, and special quadrilateral properties.

A quadrilateral is a four-sided figure. This chapter studies special quadrilaterals and uses deduction to prove their properties.

Rectangle: A quadrilateral whose angles are all \(90^\circ\). Its diagonals are equal and bisect each other.

Square: A special rectangle with all sides equal. Its diagonals are equal, bisect each other at \(90^\circ\), and bisect the angles.

Parallelogram: A quadrilateral with opposite sides parallel. Opposite sides and angles are equal; adjacent angles add to \(180^\circ\).

Change the angle between equal bisecting diagonals. The quadrilateral remains a rectangle; at \(90^\circ\), it becomes a square.

Angle between diagonals

The sum of all interior angles is \(360^\circ\).

All angles are \(90^\circ\); opposite sides are equal and parallel; diagonals are equal and bisect each other.

All sides equal, all angles \(90^\circ\); diagonals are equal, perpendicular, bisect each other, and bisect angles.

Opposite sides are parallel and equal; opposite angles are equal; adjacent angles are supplementary.

Every square is a rectangle, and every rectangle is a parallelogram.

Equal and bisecting diagonals define rectangles; equal, bisecting and perpendicular diagonals define squares.

Score: 0Current Streak: 🔥 0Badge: Quadrilateral Explorer

Set whether diagonals are equal, bisect, and perpendicular. The lab predicts the quadrilateral.

Enter three angles. The fourth angle is forced by the \(360^\circ\) sum.

A
°

B
°

C
°

D
90°

Choose one angle. The adjacent angle is supplementary and the opposite angle is equal.

Angle A

All angles are 90° and all sides are equal.

Generate printable practice on quadrilateral angle sums, rectangle/square/parallelogram properties, diagonals, and classification.

Number of problems:

Define and identify quadrilaterals, rectangles, squares, and parallelograms.
Use diagonal properties to reason about rectangles and squares.
Prove and use the angle sum of a quadrilateral as \(360^\circ\).
Use parallel-line angle properties to find angles in parallelograms.
Understand set relationships: square ⊂ rectangle ⊂ parallelogram ⊂ quadrilateral.