IMO Practice Test — Quadrilaterals
6 Questions • 10 min • Olympiad level
10:00
Question 1 of 6
hard
A quadrilateral has 4 equal sides but NO right angles. What is it?
Square
Rectangle
Rhombus
Parallelogram
Explanation: 4 equal sides + no right angles = rhombus. A square has right angles too.
Question 2 of 6
hard
A square has side 5 cm. A rectangle has the same perimeter. If rectangle length = 7 cm, width = ?
2 cm
3 cm
4 cm
5 cm
Explanation: Square P = 4x5=20. Rectangle: 2(7+W)=20, 7+W=10, W=3 cm.
Question 3 of 6
hard
Which quadrilaterals have diagonals that are equal in length?
Square and rhombus
Square and rectangle
Trapezoid and parallelogram
All quadrilaterals
Explanation: Square and rectangle both have equal diagonals. Rhombus diagonals are not equal (unless it is a square).
Question 4 of 6
hard
A shape has opposite sides equal and parallel, but angles are NOT 90°. It is a?
Rectangle
Square
Parallelogram
Trapezoid
Explanation: Opposite sides parallel and equal + angles not 90° = parallelogram (not a rectangle or square).
Question 5 of 6
hard
How many quadrilaterals have 4 right angles?
1 (only square)
2 (square and rectangle)
3 (square, rectangle, rhombus)
All quadrilaterals
Explanation: Only square and rectangle have 4 right angles. Other quadrilaterals may have different angles.
Question 6 of 6
hard
A parallelogram has angles 110°, 70°, 110°, 70°. All sides equal. What is this shape?
Rectangle
Square
Rhombus
Trapezoid
Explanation: Parallelogram with all 4 sides equal = rhombus. Since angles are not 90°, it is not a square.