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Classifying shapes: cheat sheet

Angles and shapes · The words and methods from the lessons, with an example of each.

triangles by sides and angles

Give two names: one for the sides (how many are equal) and one for the biggest angle. Equal sides sit opposite equal angles.

scalene, isosceles, equilateral    acute, right-angled, obtuse\text{scalene, isosceles, equilateral} \;\; \text{acute, right-angled, obtuse}
An isosceles acute triangle, its equal sides ticked
An isosceles acute triangle, its equal sides ticked

regular polygon

Both are needed: a rhombus has equal sides but is not regular. Names: pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.

equal sides  and  equal angles\text{equal sides} \;\text{and}\; \text{equal angles}

quadrilateral family

Trapezium: at least one pair of parallel sides. Parallelogram: two. Rhombus: four equal sides. Rectangle: four right angles. Square: both. Kite: two pairs of equal neighbouring sides. A square is also a rectangle and a rhombus.

every square is a rectangle; every rectangle is a parallelogram\text{every square is a rectangle; every rectangle is a parallelogram}
A square with equal sides, parallel sides and right angles marked
A square with equal sides, parallel sides and right angles marked

convex and concave

Convex: every corner points out. Concave: at least one corner points in.

concave: an angle>180∘\text{concave: an angle} > 180^\circ
A concave hexagon with one corner pointing in
A concave hexagon with one corner pointing in