Classifying shapes by properties · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Shape families: rectangles, squares, and more

Mathematics · Geometry · ages 10-11
Name ______________________   Date ____________

  1. A rectangle has 4 right angles. How many right angles do 3 identical rectangles have altogether?

    Answer: ______________

  2. Which statement is always true?

    • All rectangles are squares
    • All squares are rectangles
    • All trapeziums are squares
    • All rhombuses are rectangles

  3. Which shape is always a rectangle?

    • Any rhombus
    • Any square
    • Any parallelogram

  4. What do all parallelograms have in common?

    • Four right angles
    • Four equal sides
    • Two pairs of parallel sides

  5. Two opposite angles of a parallelogram are 60 degrees each. The other two angles are equal. What is each of them in degrees?

    Answer: ______________

  6. Which hierarchy correctly places these shapes from biggest group to smallest?

    • Square, then rectangle, then parallelogram
    • Rectangle, then parallelogram, then square
    • Parallelogram, then rectangle, then square

  7. Where does a square sit in a hierarchy diagram of quadrilaterals?

    • Outside all other shapes
    • Inside trapeziums only
    • Inside rectangles and inside rhombuses
    • Inside kites only

  8. Zac says all rectangles are squares because both have four right angles. Is Zac right?

    Circle one:   True   False

  9. Jun says: "This shape has 4 equal sides, so it must be a square." The shape actually has no right angles. What is Jun's mistake?

    • He forgot a square needs unequal sides
    • He forgot a square also needs 4 right angles
    • He is actually correct

  10. A quadrilateral has diagonals that bisect each other at right angles but are NOT equal. What must it be?

    • Rhombus
    • Rectangle
    • Square
    • Isosceles trapezium
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Shape families: rectangles, squares, and more W1-mt_liIW336odh-s1

  1. 12 · Altogether they have 12 right angles because 3 times 4 = 12.
  2. All squares are rectangles · All squares are rectangles is always true because every square has four right angles and opposite sides equal.
  3. Any square · A square has 4 right angles and equal opposite sides, so it always passes the rectangle test.
  4. Two pairs of parallel sides · Every parallelogram has two pairs of parallel, equal-length sides. Right angles and equal sides are extra properties only some parallelograms have.
  5. 120 · Each is 120 degrees because angles of a quadrilateral total 360: (360 - 120) / 2 = 120.
  6. Parallelogram, then rectangle, then square · Parallelogram is the biggest family. Rectangle is a special parallelogram, and square is a special rectangle.
  7. Inside rectangles and inside rhombuses · Inside rectangles and inside rhombuses is correct because a square inherits both families at once.
  8. False · Zac is wrong. Squares also need four equal sides, which most rectangles lack.
  9. He forgot a square also needs 4 right angles · Equal sides alone make a rhombus. A square needs equal sides and 4 right angles together.
  10. Rhombus · Rhombus is correct: its diagonals are perpendicular bisectors, and unequal length rules out the square.
Worksheet · LightMySky