In Grade 3 you met kinds of quadrilaterals. Now you can sort shapes using two new tools: parallel and perpendicular sides and the kinds of angles they have.
Key idea
Triangles are sorted by their largest angle: acute (all angles acute), right (one right angle) or obtuse (one obtuse angle). Quadrilaterals are sorted by parallel sides and right angles: a trapezoid has a pair of parallel sides, a parallelogram two pairs, a rectangle two pairs and 4 right angles, a rhombus 4 equal sides, and a square is both a rectangle and a rhombus.
Why it works
A name is a promise about attributes. "Rectangle" promises 4 right angles. A square keeps that promise (and also has equal sides), so every square is a rectangle, but not every rectangle is a square. The best name is the one that promises the most.
Worked example: Sort a triangle
A triangle has angles of $30^\circ$, $60^\circ$ and $90^\circ$. What kind is it?
- It has a $90^\circ$ angle.
Answer: A right triangle
Worked example: The best name
A quadrilateral has 2 pairs of parallel sides, 4 equal sides and no right angles. What is the best name?
- 2 pairs of parallel sides: a parallelogram.
- 4 equal sides: a rhombus. No right angles, so not a square.
Answer: Rhombus
Some books say a trapezoid has exactly one pair of parallel sides; others say at least one pair. Problems here only call a shape a trapezoid when it has exactly one pair.