Classifying triangles & quadrilaterals

Triangles can be classified by their sides or angles. By sides: equilateral (all 3 sides equal), isosceles (2 sides equal), scalene (no sides equal). By angles: acute (all angles under 90°), right-angled (one angle exactly 90°), obtuse (one angle over 90°). Quadrilaterals (4-sided shapes) also have their own properties: a square has 4 equal sides and 4 right angles; a rectangle has 4 right angles but only opposite sides equal; a parallelogram has opposite sides equal and parallel; a rhombus has 4 equal sides but angles that aren't necessarily 90°; a trapezium has exactly one pair of parallel sides.

Key terms

Equilateral triangle:

A triangle with all 3 sides equal.

Isosceles triangle:

A triangle with 2 sides equal.

Parallelogram:

A quadrilateral with opposite sides equal and parallel.

Questions

1. 1. An equilateral triangle has:

   • No equal sides
   • 2 equal sides
   • 3 equal sides
   • 4 equal sides

2. 2. An isosceles triangle has:

   • No equal sides
   • Exactly 2 equal sides
   • 3 equal sides
   • 4 equal sides

3. 3. A scalene triangle has:

   • 3 equal sides
   • 2 equal sides
   • No equal sides
   • 4 equal sides

4. 4. A right-angled triangle has one angle of:

   • 45°
   • 60°
   • 90°
   • 180°

5. 5. A square has:

   • 3 equal sides
   • 4 equal sides and 4 right angles
   • No right angles
   • 5 sides

6. 6. A rectangle has:

   • 4 equal sides always
   • 4 right angles
   • No right angles
   • 3 sides

7. 7. A parallelogram has:

   • No parallel sides
   • Opposite sides equal and parallel
   • Only 3 sides
   • All sides equal

8. 8. A triangle with angles 60°, 60°, 60° is:

   • Scalene
   • Isosceles
   • Equilateral
   • Obtuse

9. 9. A triangle with sides 4cm, 4cm, 7cm is:

   • Equilateral
   • Isosceles
   • Scalene
   • Right-angled

10. 10. An obtuse triangle has one angle that is:

    • Less than 90°
    • Exactly 90°
    • Greater than 90°
    • Exactly 180°

11. 11. A rhombus has:

    • 4 equal sides, but angles not necessarily 90°
    • 4 right angles always
    • Only 2 equal sides
    • No equal sides

12. 12. A trapezium has:

    • 4 equal sides
    • Exactly one pair of parallel sides
    • No sides at all
    • 4 right angles

13. 13. A shape with 4 equal sides and angles of 70° and 110° is a:

    • Square
    • Rectangle
    • Rhombus
    • Trapezium

14. 14. All squares are also:

    • Triangles
    • Rectangles
    • Trapeziums
    • Circles

15. 15. Is every rectangle also a parallelogram?

    • Yes
    • No
    • Only sometimes
    • Only if it's a square

16. 16. Is every square also a rhombus?

    • Yes
    • No
    • Only sometimes
    • Never

17. 17. A triangle has angles of 90°, 45°, 45°. How would you classify it by both angle AND side type?

    • Scalene and acute
    • Isosceles and right-angled
    • Equilateral and obtuse
    • Scalene and obtuse

18. 18. Which shape must have exactly one pair of parallel sides, not two?

    • Parallelogram
    • Trapezium
    • Rhombus
    • Square

19. 19. Can a triangle have two right angles?

    • Yes, always
    • No, since angles must sum to 180°
    • Only in isosceles triangles
    • Only in equilateral triangles

20. 20. A quadrilateral has 4 equal sides and 4 right angles. What is the most specific name for it?

    • Rhombus
    • Rectangle
    • Square
    • Trapezium