Classifying Triangles and Quadrilaterals by Properties

Triangles are named by their sides. Three equal sides is equilateral, two equal is isosceles, none equal is scalene. Equal sides sit opposite equal angles, so an equilateral triangle also has three sixty-degree angles and an isosceles triangle has two equal angles. Sides of five, five and eight make an isosceles triangle; three, four and five make a scalene one. On a drawing, read the tick marks rather than judging by eye.

Triangles are also named by their angles: acute when all three are under ninety, right when one is exactly ninety, obtuse when one is more. A triangle can have at most one such angle, because all three add to a hundred and eighty. Every triangle therefore gets two names, one from each list — ninety, forty-five, forty-five is a right isosceles triangle, and a hundred and twenty, forty, twenty is an obtuse scalene one. An equilateral triangle is always acute.

Quadrilaterals are sorted by how many pairs of parallel sides they have. Parallelograms, rhombuses, rectangles and squares have two pairs; a trapezium has one; a kite has none. Parallel means the sides never meet however far you extend them, and the little arrows on a drawing mark a parallel pair. A kite does have two pairs of equal sides, which is a different thing — equal is not parallel, and which shape has no parallel sides is a favourite test question with the kite as its answer.

The names are nested, one inside another. A square has four equal sides and four right angles, so it is a rhombus, a rectangle and a parallelogram all at once. Every square is a rectangle, but not every rectangle is a square, which is why questions phrase things as always or sometimes. To test whether every A is a B, try to draw an A that is not a B: a five-by-two rectangle is not a square, so the answer there is no.

Treat a description as a list of properties and check them one at a time. Four equal sides and no right angles is a rhombus. Two pairs of parallel sides and four right angles is a rectangle, and a square if the sides are equal too. When two shapes fit, the question wants the one that fits exactly, so read to the end before choosing. Quiz and exercises now.