Discover Mathematics P5: Term 2, Unit 10, Lessons 1–4
GoalSort polygons and quadrilaterals into categories by their sides, parallel sides and angles.
New words
polygon · a closed flat shape made only of straight sidesparallel · two lines that stay the same distance apart and never meetcategory · a group of shapes that share an attributerhombus · a quadrilateral with 4 equal sides
Explanation
A polygon is a closed flat shape with straight sides. We name it by its number of sides: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, octagon 8. A quadrilateral has many families. A trapezium has one pair of parallel sides. A parallelogram has two pairs of parallel sides, and its opposite sides are equal. A rectangle is a parallelogram with 4 right angles. A rhombus is a parallelogram with 4 equal sides. A square has 4 equal sides and 4 right angles, so it is a rectangle and a rhombus at the same time. A kite has two pairs of equal sides that are next to each other. A shape can belong to more than one category, so always check the attributes one by one: how many sides, which sides are parallel, which are equal, and whether the angles are right angles.
Shape
Parallel pairs
4 equal sides
4 right angles
Trapezium
1
no
no
Parallelogram
2
no
no
Rectangle
2
no
yes
Rhombus
2
yes
no
Square
2
yes
yes
Worked examples
This shape has 4 equal sides and 4 right angles, so it is a square. It is also a rectangle, a rhombus, a parallelogram and a quadrilateral. The best name is the most exact one: square.
This shape has 4 equal sides but no right angles. Opposite sides are parallel. It is a rhombus, and also a parallelogram, but it is not a rectangle.
This shape has two pairs of parallel sides (the arrows) but its sides are not all equal and it has no right angles. It is a parallelogram only. Its neighbour, the trapezium, has just one pair of parallel sides.
Class activity
Shape hunt. Look around your home or classroom and find one example of each: rectangle, square, parallelogram or rhombus (a tile, a kite, a picture frame, a road sign), trapezium and pentagon. Sketch each one and write two attributes that prove its name.
Practice
1
A shape has 4 sides, two pairs of parallel sides, equal opposite sides, no right angles, and its sides are not all equal. Name it.
A parallelogram.
2
True or false? (a) Every rectangle is a parallelogram. (b) Every parallelogram is a rectangle.
(a) True: it has two pairs of parallel sides. (b) False: a parallelogram may have no right angles.
3
Which of these always have 4 equal sides: square, rectangle, rhombus, kite, trapezium?
The square and the rhombus.
4
Name the polygon with 5 sides, the one with 6 sides and the one with 8 sides.
Pentagon, hexagon, octagon.
5
Nour says a square is not a rectangle because its sides are all equal. Is she right?
No. A rectangle needs 4 right angles and equal opposite sides. A square has all of these, so a square is a special rectangle.
