Week 8 · Fact families and quadrilaterals · 3 lessons
3
Trapeziums and rhombuses
Discover Mathematics P3: Term 1, Lessons 21–30
GoalRecognise a trapezium by its parallel sides and a rhombus by its four equal sides.
New words
parallel · lines that stay the same distance apart and never meettrapezium · a quadrilateral with one pair of parallel sidesrhombus · a quadrilateral with four sides of equal length
Explanation
Parallel sides are like the two edges of a straight road or a railway. They stay the same distance apart and never meet. Small arrows on two sides show that they are parallel. A trapezium is a quadrilateral with one pair of parallel sides, and its other two sides are not parallel. A rhombus is a quadrilateral with four sides of equal length. Its opposite sides are also parallel, and it looks like a tilted square, or a diamond. To check a rhombus, measure all four sides with a ruler. To check a trapezium, look for one pair of sides that run in the same direction.
Worked examples
This is a rhombus. Measure each side: all four are 4 cm. The opposite sides are parallel, and the shape looks like a tilted square.
This is a trapezium. The top side is 3 cm and the bottom side is 7 cm. The two arrows show that they are parallel. The two slanted sides are not parallel.
This quadrilateral has no pair of parallel sides and its four sides are not all equal. It is not a trapezium and it is not a rhombus. It is just a quadrilateral.
Class activity
Straw rhombus. Take 4 strips of card or 4 straws of the same length. Join the ends loosely with paper clips or tape to make a four-sided shape. Push it so it leans one way, then the other. Does it always have 4 equal sides? Look around your home for parallel lines, such as the edges of a shelf or a road.
Practice
1
Which two sides are parallel?
AB and DC, the two sides with arrows.
2
How many pairs of parallel sides does a trapezium have?
One pair.
3
This rhombus has one side of 5 cm. How long are the other three sides?
5 cm each, because all four sides of a rhombus are equal.
4
Marina says every quadrilateral is a rhombus. Is she right?
No. A rhombus needs four equal sides. A trapezium or a rectangle that is not a square is a quadrilateral but not a rhombus.
5
Draw a trapezium and mark its parallel sides with arrows.
Any four-sided shape with one pair of parallel sides marked with matching arrows and two sides that are not parallel.
