Angles and the properties of shapes
Maths · Key Stage 2 · The School
An angle is a turn
An angle measures TURN, not length — the two arms can be drawn long or short and the angle is the same. A quarter turn is 90° and is called a RIGHT ANGLE. Less than that is ACUTE, more than 90° but less than 180° is OBTUSE, and more than 180° is REFLEX. A straight line is 180°, a full turn 360°.
Sorting shapes by what is true of them
Triangles are named by their sides or angles: EQUILATERAL has three equal sides, ISOSCELES two, SCALENE none, and a RIGHT-ANGLED triangle contains a 90° angle. Quadrilaterals are sorted by parallel sides and equal angles: square, rectangle, rhombus, parallelogram, trapezium, kite. A square is also a rectangle and also a rhombus — the categories overlap on purpose.
Symmetry
A shape has a LINE OF SYMMETRY where a mirror placed along it would show the shape unchanged. A square has four, a rectangle two, an equilateral triangle three, and a circle infinitely many. A parallelogram that is not a rectangle has none at all, which surprises people because it looks so regular — a good reminder to test rather than assume.
A triangle has sides of 5 cm, 5 cm and 8 cm, and one angle of 106°. By SIDES: two are equal, so it is isosceles. By ANGLES: one is more than 90°, so it is obtuse. Both names are correct at once, because they answer different questions. Check the angles add to 180°: 106° + 37° + 37° = 180°. And the two equal angles sit opposite the two equal sides — always, in every isosceles triangle.