GCSE · Maths · AQA · Spec 8300
Properties of quadrilaterals, triangles and plane figures
Turn a square onto one corner. Is it still a square? If you hesitated, this lesson is for you: shapes are named by their sides and angles, not their look.
Maths · Geometry
Always true here: DC is parallel to AB
Because DC stays parallel to AB, ∠A + ∠D = 180° and ∠B + ∠C = 180° in every position. When DC is also the same length as AB, the shape is a parallelogram — and then DA = BC, ∠A = ∠C and ∠B = ∠D too.
Only the point you drag moves. Try this: (1) Drag C a little — which readings stop matching? Drag it back until DC is 5.0 cm again. (2) Put D directly above A and C directly above B. (3) Now drag B until AB is 4.0 cm and line C up above B again. (4) Challenge: make all four sides 5.0 cm with no right angles. (Hint: put D 3 cm to the right of A.)
Triangles
Every triangle has two names
Sort each triangle by its sides. Then switch the rule and sort the same triangles by their angles.
Equal angles sit opposite equal sides. So how many sides are equal?
Still to sort
Scalene (0)
No equal sides, so no equal angles.
Isosceles (0)
Two equal sides, and the two angles opposite them are equal.
Where the line is: An equilateral triangle has equal sides too, but its most precise name is equilateral, because all three sides are equal.
Equilateral (0)
Three equal sides and three equal angles of 60°.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Name a shape by what is true about it — never by how it looks.
What you need to know
- A shape's name comes from its properties — its side lengths, angles and parallel sides — not from how it looks or which way it is turned.
- A parallelogram has two pairs of parallel sides, so its opposite sides are equal and its opposite angles are equal.
- A rectangle has four right angles and a rhombus has four equal sides. A square has both, so a square is also a rectangle, a rhombus and a parallelogram.
- A kite has two pairs of equal sides, each pair next to each other. A trapezium has one pair of parallel sides.
- Every triangle has a name from its sides (scalene, isosceles, equilateral) and a name from its angles (acute-angled, right-angled, obtuse-angled).
- Polygons are named by their number of sides: pentagon 5, hexagon 6, octagon 8, decagon 10. A regular polygon has all sides equal and all angles equal.
The big picture
A shape's name comes from its properties, not its look. A parallelogram has two pairs of parallel sides, so opposite sides and opposite angles are equal. Add four right angles and it's a rectangle; add four equal sides and it's a rhombus; a square has both, so it is all three. A kite has two pairs of equal adjacent sides; a trapezium has one pair of parallel sides. Every triangle has a side-name (scalene, isosceles, equilateral) and an angle-name (acute-, right- or obtuse-angled). Polygons are named by side count: pentagon 5, hexagon 6, octagon 8, decagon 10.
Key points
Worked example
Problem
Quadrilateral ABCD has AB = AD = 5 cm and CB = CD = 8 cm. (a) Name the quadrilateral. (b) Angle ABC = 100°. Write down the size of angle ADC, and give a reason.
⚠ Watch out
Thinking a rectangle must have two long sides and two short sides. A rectangle only needs four right angles — so a shape with four right angles and four equal sides is a rectangle as well as a square.
Memory hook
Think of a family tree. Every Labrador is a dog, but not every dog is a Labrador. In the same way, every square is a rectangle, but not every rectangle is a square — and 'parallelogram' is the family name that the rectangle, rhombus and square all share.
Check yourself
A quadrilateral has four right angles and sides of 5, 9, 5 and 9 cm. Name two special quadrilaterals it is, and one it isn't. (Rectangle and parallelogram; not a square: unequal sides.)
Flashcards
(11)What decides the name of a shape?
What must a parallelogram have, and what follows from it?
Is a square a rectangle?
Rhombus or square — what is the difference?
Kite: which sides are equal?
What is a trapezium?
Which special quadrilaterals always have diagonals of equal length?
Isosceles triangle: what is equal?
How do you decide between acute-angled, right-angled and obtuse-angled?
How many sides: pentagon, hexagon, octagon, decagon?
What does 'regular' mean for a polygon?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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