Module 6 of 6 · MA4-GEO-C-01
Triangles & quadrilaterals
Solve numerical problems using properties of triangles and quadrilaterals
01
The two angle sums
The three angles of any triangle add to 180°. The four angles of any quadrilateral add to 360° — which you can prove by cutting the quadrilateral into two triangles with a diagonal.
02
Isosceles triangles
If two sides are equal then the two angles opposite them are equal — the base angles. Read this backwards too: if two angles are equal, the triangle is isosceles. An equilateral triangle has all three angles 60°.
03
The exterior angle
An exterior angle of a triangle equals the sum of the two interior opposite angles. It saves a step whenever a side of the triangle is extended in the diagram.
04
Special quadrilaterals
In a parallelogram opposite angles are equal and co-interior angles add to 180°. A rhombus is a parallelogram with four equal sides. A kite has one pair of equal opposite angles — the ones between the unequal sides.
The rules to know by heart
- Angle sum of a triangle180°
- Angle sum of a quadrilateral360°
- Base angles of an isosceles triangleare equal
- Equilateral triangleevery angle is 60°
- Exterior angle of a triangleequals the sum of the two interior opposite angles
- Opposite angles of a parallelogramare equal
See it work
Try it — tick every property that is always true
| Parallelogram | Rectangle | Rhombus | Square | Trapezium | Kite | |
|---|---|---|---|---|---|---|
| Opposite sides are parallel | ||||||
| Opposite sides are equal | ||||||
| All four sides are equal | ||||||
| All angles are 90° | ||||||
| Opposite angles are equal | ||||||
| Diagonals are equal | ||||||
| Diagonals bisect each other | ||||||
| Diagonals meet at right angles |
Notice the square's column: every tick a rectangle has, and every tick a rhombus has. That is why a square can be called all three.
A worked example
Find the size of angle x, and give the reason.
Worked solution
- 73° + 45° + x = 180°(angle sum of a triangle is 180°)
Every line has its reason in brackets. In the test, that bracket is worth marks on its own — write it even when the number feels obvious.
Words for this module
Types of triangle
Scalene (no equal sides), isosceles (2 equal), equilateral (3 equal, all 60°). Also acute-, right- and obtuse-angled.
Watch out: A triangle can have two names at once, like right-angled isosceles.
Special quadrilaterals
Parallelogram, rectangle, rhombus, square, trapezium, kite — each defined by its side, angle and diagonal properties.
Watch out: A square is a rectangle AND a rhombus AND a parallelogram. The names overlap on purpose.
Angle sum
Triangle = 180°. Quadrilateral = 360°.
Exterior angle of a triangle
Equals the sum of the two interior opposite angles.
ready?
Practise until you get five in a row.