Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category
You have sorted quadrilaterals by their sides before: how many, how long, which ones match. The lines themselves give you a second way to sort. Two sides are parallel when they run the same way and never meet, however far you stretch them. On a plan, matching arrows mark a parallel pair. A rectangle has two pairs of parallel sides, and so does a square. A triangle has only three sides, so it can never make two pairs.
Omar holds the corner of a book page against one corner of a triangle. It fits exactly, so that corner is a right angle, and the two sides meeting there are perpendicular. On a drawing, a small square inside the corner is the mark for a right angle. One right angle is enough to call the whole shape a right triangle. The other two corners can be any size.
Now sort with both clues at once. A square shows both: its opposite sides are parallel, and every corner is a right angle, so sides that meet there are perpendicular. A right triangle shows only one. Its two sides at the square corner are perpendicular, but none of its three sides run parallel to another. So a right angle does not promise parallel sides.
Sorting fast: hunt for the arrows first, then the square corners. Two sides that lean towards each other are not parallel, even if they have not met yet on the page.
Sort shapes by their lines: arrows mark a parallel pair, a small square marks a right angle, and the two clues can turn up together, one at a time, or not at all.
The new play area is still a plan on paper. You have already sorted its shapes by their side rules: how many sides, which ones match. Mia wants to sort the same plan a second way, by the lines.
The sandpit is drawn as a rectangle. How many pairs of parallel sides does it have?
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.