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.
Quadrilaterals sort by their parallel sides. Parallelograms, rectangles, rhombuses, and squares keep two pairs. Trapezoids keep exactly one pair. Kites and arrowheads keep none. Sort with two questions. Does it have any parallel sides? If yes, how many pairs? The answers drop each quadrilateral into its home group.
Polygons also sort by angles. Right triangles hold one 90 degree corner, which you can test with the corner of a book. Acute triangles hold only sharp corners, obtuse triangles hold one wide corner. A triangle cannot hold two right angles. Two square corners would need 180 degrees, leaving nothing for the third corner.
Side lengths add a second sorting key. Equilateral triangles have 3 equal sides, isosceles have 2, and scalene have none equal. The 3, 4, 5 triangle is scalene and right at the same time. Combine both keys for a full description. A 3, 4, 5 triangle is a scalene right triangle. Names stack: sides first, angles second.
Rectangles are rich in line properties. They hold two pairs of parallel sides and four perpendicular corners. That makes them perfect examples of shapes with both parallel and perpendicular sides. Circles sit at the other extreme with no straight sides at all. When asked for shapes with both properties, reach for rectangles, squares, and right trapezoids.
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.