Diagonals of quadrilaterals
Draw both diagonals of quadrilaterals and investigate, by measuring or folding, whether in that figure the diagonals are equal in length, whether either or both bisect the other, and whether they meet at right angles; build a property list from the investigation and use it in spatial arguments — for example, every parallelogram's diagonals bisect each other, every rectangle's are equal, every rhombus's are perpendicular bisectors of each other, and in a kite one diagonal bisects the other (both may do so in special cases such as a rhombus, but a kite that is not a rhombus shows that mutual bisection is not guaranteed); recognise that shape classes include one another (a square is a rectangle, a rhombus and a kite), so properties are checked on the actual figure rather than assumed from a name
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Diagonals of quadrilaterals means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper shapes or a ruler and pencil; Shape or angle name cards. 1. Say the goal of Diagonals of quadrilaterals in plain words once. 2. Adult traces or shows one shape/angle and names a key property. 3. Child measures or classifies three shapes/angles and names a property each time. 4. Fresh check: one fresh property name. Record and stop. Done: three correct property names with a sketch or measure. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
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Area Builder supports hands-on exploration for Diagonals of quadrilaterals. Not every lab worksheet.
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Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Draw the diagonals of several quadrilaterals (including a square, a non-square rectangle, a non-square rhombus, a parallelogram, a kite that is not a rhombus and a trapezoid), measure them and the angle where they cross, and record in a table which pairs are equal, bisect each other or are perpendicular
- Use a measured counterexample to show that a diagonal property does not by itself identify a shape — for example, equal diagonals occur in every rectangle, not only in squares, and a kite that is not a rhombus has only one diagonal cut in half by the other
- Use diagonal properties in a spatial argument, such as deciding which quadrilaterals could have diagonals that are equal and bisect each other, or explaining why diagonals that are perpendicular bisectors of each other show a rhombus
“If your child draws lines from corner to corner across a kite-shaped piece of paper, can they measure or fold to check which line is cut exactly in half and whether the lines cross at a right angle — rather than guessing from the shape's name?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 11–12
Standards