Discover Mathematics P4: Term 2, Unit 12, Lessons 11–14
GoalName quadrilaterals by their properties and find them in real objects.
New words
quadrilateral · a polygon with 4 sides and 4 verticesparallelogram · a quadrilateral with two pairs of parallel sidestrapezoid · a quadrilateral with exactly one pair of parallel sidesrhombus · a quadrilateral with 4 equal sides
Explanation
A quadrilateral is a polygon with four sides. We name quadrilaterals by their properties: parallel sides, equal sides and right angles. A parallelogram has two pairs of parallel sides. A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four equal sides. A square has four equal sides and four right angles, so it is both a rectangle and a rhombus. A trapezoid has exactly one pair of parallel sides. We find these shapes in the real world: a tray is a rectangle, a floor tile can be a rhombus or a square, and the side of a bucket is a trapezoid. To name a shape, ask: how many pairs of parallel sides? Are all sides equal? Are there right angles?
Shape
Parallel pairs
Equal sides
Right angles
square
2
all 4
4
rectangle
2
opposite sides
4
rhombus
2
all 4
not needed
parallelogram
2
opposite sides
not needed
trapezoid
1
not needed
not needed
Worked examples
Rhombus or square? This shape has four equal sides (the ticks) and opposite sides that are parallel, but its corners are not square corners. So it is a rhombus, not a square. A square is a rhombus with right angles.
Find the shapes in daily life. A bakery tray is a rectangle, a floor tile is a rhombus and the side of a bucket is a trapezoid, because its top and bottom are parallel but its slanted sides are not.
Name the shape from clues. Clue: 4 sides, 2 pairs of parallel sides, opposite sides equal, no right angles. This is a parallelogram. The marks show the two pairs of parallel sides.
Class activity
Shape detectives. Look around your kitchen or classroom for quadrilaterals. Find at least one example of a square, a rectangle, a rhombus (or a diamond shape), a parallelogram and a trapezoid. Draw each one and write its clues: pairs of parallel sides, equal sides and right angles.
Practice
1
Name the quadrilateral with four equal sides and four right angles.
A square.
2
Name the quadrilateral that has exactly one pair of parallel sides.
A trapezoid.
3
Is every rectangle a parallelogram? Why?
Yes. A rectangle has two pairs of parallel sides, which is what a parallelogram needs.
4
The shape has two pairs of parallel sides, opposite sides equal, and no right angles. Its sides are not all equal. What is it?
A parallelogram.
5
Seif says every square is a rectangle. Is he right?
Yes. A square has four right angles and opposite sides that are equal and parallel, so it is a special rectangle.
