Understand that shapes in different categories may share attributes defining a larger category; classify quadrilaterals (rhombuses, rectangles, squares) and draw examples of quadrilaterals not in those subcategories
A quadrilateral is any shape with exactly four straight sides. Four sides means four angles, so every quadrilateral has four corners too. Squares, rectangles, and rhombuses are all quadrilaterals, but each one passes an extra test. Those tests ask about right angles. A right angle is a square corner, the shape you see in the corner of a page.
A rectangle only needs four right angles. Its sides can be different lengths, as long as opposite sides match. A rhombus only needs four equal sides. Its angles can lean, as long as opposite angles match each other. A square needs both: four equal sides and four right angles.
Picture a patch of playground 8 metres along the top and 5 metres down the side. Every corner is a right angle, so it follows the rectangle rule. But 8 and 5 are not equal, so it does not follow the rhombus rule, and it is not a square.
A square passes the rectangle test and the rhombus test at the same time, so it earns all three names at once. Picture circles: the quadrilateral circle holds every four-sided shape, with a smaller rectangle circle and a smaller rhombus circle inside it. The square sits where those two smaller circles overlap.
You can also draw a quadrilateral that skips every special rule. Draw four straight sides that join up, with no side matching another and no square corners. A kite or a slanted four-sided shape works. It still belongs in the quadrilateral circle, and nowhere smaller.
A square is always a rectangle and always a rhombus, but not every rectangle or rhombus is a square, and not every quadrilateral is either one.
You already found that a shape's sides and its angles come in the same number: four straight sides, four corners. Mia, Zara, and Omar are planning a new play area for the playground. It gets drawn on paper first, one patch of paint per shape.
Rule one at the top of the plan says every patch must be a quadrilateral. What does a patch need to pass that rule?
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.