Primary 5 maths · Geometry · About 12 minutes
Use parallelogram, rhombus and trapezium properties
Identify the relevant property before combining angle facts. Do not invent extra lines or equalities.
Start the interactive lesson →Open practice activity
What you will learn
- Use parallelogram, rhombus and trapezium properties
Models used: number sentences, stories, tables.
Before you start
A turn does not change the shape
Look for straight sides, corners and curved boundaries.
Look for straight sides, corners and curved boundaries.
Follow the sides and corners. Turn the shape. Its sides are still the same length, and its corners have the same openings.
Turning a figure changes where it points. It keeps its side lengths and corner angles, so it is still the same shape.
Follow the sides and corners. The same figure, turned through 25 degrees. Use those features to recognise the shape, whichever way it is turned.
Turning a figure changes where it points. It keeps its side lengths and corner angles, so it is still the same shape.
Follow the sides and corners. Changing orientation preserves the shape.
What did the picture help us see?
Use those features to recognise the shape, whichever way it is turned.
Worked example: A new example, together
In a parallelogram, one angle is 30°. Find its adjacent interior angle x.
| Known angle | Relationship |
|---|---|
| 30° | angles in the named geometric figure |
Use only the stated lines and properties. Read each value with the heading above its column.
Identify the relevant property before combining angle facts. Do not invent extra lines or equalities.
Adjacent angles of a parallelogram are supplementary.
Use only the stated lines and properties Known angle Relationship 30° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
Opposite sides of a parallelogram are parallel.
Use only the stated lines and properties Known angle Relationship 30° angles in the named geometric figure In a parallelogram, one angle is 30°. Find its adjacent interior angle x.
150 degrees
Use only the stated lines and properties. Read each value with the heading above its column.
Adjacent interior angles between parallel sides sum to 180°.
Use only the stated lines and properties Known angle Relationship 30° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
x = 180 − 30 = 150°.
Use only the stated lines and properties Known angle Relationship 30° angles in the named geometric figure Use only the stated lines and properties. Read each value with the heading above its column.
Check the result against the question we started with.
30 + 150 = 180°.
We found 150 degrees. Adjacent angles of a parallelogram are supplementary.
Use only the stated lines and properties Known angle Relationship 30° angles in the named geometric figure
Common mistakes to discuss
- Every quadrilateral behaves alike. Each has its own properties. In a parallelogram opposite angles are equal and neighbouring angles total 180°; a trapezium needs only one pair of parallel sides.
Check your understanding
- Use parallelogram, rhombus and trapezium properties
- connect shape properties with justified angle calculations
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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