Quadrilaterals – identifying special shapes

What it shows

Special quadrilaterals form a family defined by their properties. A trapezoid has a pair of parallel sides; a parallelogram has two pairs; a rectangle is a parallelogram with a right angle, a rhombus has four equal sides, and a square is both a rectangle and a rhombus. The simulation measures the sides, angles and diagonals of the quadrilateral ABCD you draw, ticks the properties that hold, such as diagonals that bisect each other or are perpendicular, and names the most specific shape, including right and isosceles trapezoids and non-convex quadrilaterals.

How to use

Choose a Starting shape, for example Parallelogram, and drag the vertices A, B, C, D. Keep Snap vertices to the grid on so that parallel sides and right angles are easy to build. With Show the two diagonals and Show side lengths and angles on, change one feature at a time and watch the checklist and the shape name: when do the diagonals become equal, and what does the parallelogram turn into?

Parameters you can change

• Starting shape Any quadrilateral, Trapezoid, Isosceles trapezoid, Parallelogram, Rectangle, Rhombus, Square
• Show the two diagonals
• Show side lengths and angles
• Snap vertices to the grid

Questions to explore

1. Is a quadrilateral with one pair of parallel sides and two equal other sides always an isosceles trapezoid?
2. What does a parallelogram become when its diagonals are perpendicular? What if they are equal in length?
3. Which conditions on the diagonals alone are enough to make a quadrilateral a square?