Primary 5 Parallelogram, Rhombus and Trapezium Study Guide
Four short steps for the last Primary 5 geometry chapter: read the marks, use the properties, find unknown angles, then draw on a grid. Each step has something to tap, followed by worked examples and a five-question check.
Start here
What are a parallelogram, a rhombus and a trapezium?
They are four-sided figures, and the marks on their sides tell them apart.
Matching arrowheads show sides that are parallel. Ticks show sides of equal length. A trapezium has exactly one pair of parallel sides. A parallelogram has two pairs, and its opposite sides are equal. A rhombus is a parallelogram with all four sides equal. Your child reads the marks first, names the shape, then uses what is true of it.
In this chapter, your child learns to:
- read arrowheads and ticks on a four-sided figure;
- name a trapezium, a parallelogram or a rhombus from its marks;
- find a missing side using the properties of the shape;
- find unknown angles without drawing extra lines;
- complete these figures on a square or dot grid.
Step 1
How to tell a parallelogram, rhombus and trapezium apart
Arrowheads mean parallel; ticks mean equal. Sides with the same arrowheads are parallel. A second pair of parallel sides gets its own arrowheads, often two on each side. Sides with the same ticks are equal in length. Count the pairs of arrowheads, check for ticks, and the name follows. Read the marks rather than the look of the figure.
A four-sided figure has matching arrowheads on one pair of sides and no other marks. What is it?
Step 2
Properties of a parallelogram, rhombus and trapezium
Name the shape first, then use what is true of it. In a parallelogram, opposite sides are parallel and equal in length. A rhombus has that too, and all four of its sides are equal. A trapezium has exactly one pair of parallel sides; its marks tell you nothing more about its lengths. Write the property in brackets after the line that uses it.
Tap Next step
WXYZ is a parallelogram. WX = 7 cm and its perimeter is 26 cm. How long is XY?
Step 3
Finding unknown angles in a parallelogram and trapezium
Between two parallel sides, the two angles add up to 180°. Pick a pair of parallel sides and a side that joins them. The two angles along that joining side add up to 180°. In a parallelogram or a rhombus, opposite angles are also equal. A trapezium has only one parallel pair, so only the angles between that pair add up to 180°, and its opposite angles need not be equal.
Tap Next step
EFGH is a rhombus. Angle EFG is 128°. What is angle FGH?
Step 4
Drawing shapes on a grid: parallelograms and squares
Count across, then count up. A parallel side has the same counts. To copy a slanted side, count its squares across (the run) and up or down (the rise). A side parallel to it has the same run and the same rise. Twice as long means double both counts. For a right angle, as at a corner of a square, swap the two counts and turn the direction. Then check the finished figure against every mark the question gives.
Tap Next step
On a square grid, J is at (2, 3), K is at (5, 4) and L is at (6, 7). JKLM is a parallelogram. Where is M?
Primary 5 parallelogram, rhombus and trapezium questions, worked step by stepWork each one out on paper with the figure sketched. Open the hint if you are stuck, then one line at a time.
ABCD is a parallelogram. AB = 14 cm and BC is 5 cm shorter than AB. Find the perimeter of ABCD.
- BC = 14 − 5 = 9 cm
- CD = AB = 14 cm and DA = BC = 9 cm (opposite sides of a parallelogram)
- perimeter = 14 + 9 + 14 + 9 = 46 cm
WXYZ is a parallelogram. ∠XWZ = 71°. Find ∠WXY and ∠XYZ.
- ∠WXY = 180° − 71° = 109° (angles between parallel sides)
- ∠XYZ = ∠XWZ = 71° (opposite angles of a parallelogram)
PQRS is a trapezium with PQ parallel to SR. ∠SPQ is 3 times ∠PSR. Find ∠PSR.
- ∠PSR = 1 unit, ∠SPQ = 3 units
- 1 unit + 3 units = 4 units = 180° (angles between parallel sides)
- 1 unit = 180° ÷ 4 = 45°
ABCD is a parallelogram. E is a point on DC, and the line AE is drawn. ∠DAE = 34° and ∠ABC = 68°. Find (a) ∠AED, (b) ∠EAB.
- ∠ADC = ∠ABC = 68° (opposite angles of a parallelogram)
- ∠AED = 180° − 34° − 68° = 78° (angle sum of a triangle)
- ∠DAB = 180° − 68° = 112° (angles between parallel sides)
- ∠EAB = 112° − 34° = 78°
On a square grid, E is at (1, 1), F is at (9, 3) and G is at (8, 6). EFGH is a trapezium in which HG is parallel to EF and HG is half as long as EF. Find the coordinates of H.
- EF: 8 right, 2 up
- HG is half as long: 4 right, 1 up
- so H is 4 left and 1 down from G
- H is at (4, 5)
Step 5
Check yourself
Five quick questions on marks, sides, angles and grids. Nothing is stored, and each reply points to the practice that fits.
1. A four-sided figure has two pairs of parallel sides, and all four sides are equal. What is it?
2. ABCD is a parallelogram. AB = 12 cm and BC = 7 cm. How long is CD?
3. KLMN is a parallelogram. Angle KLM is 104°. What is angle LMN?
4. ABCD is a trapezium with AB parallel to DC. Angle ABC is 65°. What is angle BCD?
5. On a grid, side PQ runs 3 right and 2 up. Side SR is parallel to PQ and twice as long. How does SR run?
Using this guide at home. Before your child answers anything, ask them to point at each mark on the figure and say what it means: these two sides are parallel, these two are equal. Naming the shape from its marks, out loud, is most of the work in this chapter.
For angle questions, ask which two sides are parallel and which angles sit between them, and encourage a short reason in brackets after each line. On a grid, a pencil walk works well: count across, then up, for one side, and walk the same counts from the next corner.
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