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

Sorting Shapes by Their Lines

Mathematics · Geometry · ages 9-10
Name ______________________   Date ____________

  1. A right triangle has one right angle. How many degrees is that angle?

    Answer: ______________

  2. Which quadrilateral has two pairs of parallel sides?

    • A trapezoid
    • A kite
    • A parallelogram
    • An arrowhead

  3. Which of these shapes always has two pairs of parallel sides?

    • Rectangle
    • Right triangle
    • A shape with three unequal sides

  4. A square has both parallel sides and perpendicular sides.

    Circle one:   True   False

  5. A rectangle has 4 right angles. How many right angles do two rectangles have?

    Answer: ______________

  6. A triangle has angles of 90 degrees, 60 degrees, and 30 degrees. Is it a right triangle?

    • No, because not all angles are 90 degrees
    • Yes, because one angle is 90 degrees
    • No, because it has three different angles

  7. Which triangle is a right triangle?

    • Sides 3, 4, 5
    • Sides 2, 3, 4
    • Sides 4, 5, 6
    • Sides 2, 4, 6

  8. Ben says a triangle can have two right angles. Is Ben right?

    Circle one:   True   False

  9. Ben says, 'This shape has perpendicular sides, so it must also have parallel sides.' Is Ben always correct?

    • Yes, any shape with a right angle also has parallel sides
    • No, perpendicular and parallel sides always come together
    • No, a right triangle has perpendicular sides but no parallel sides

  10. A square and a rectangle together have how many right angles?

    Answer: ______________

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Answer key

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

Sorting Shapes by Their Lines W1-mt_r8c43QB6wx-s1

  1. 90 · A right angle is 90 degrees.
  2. A parallelogram · A parallelogram has two pairs of parallel sides.
  3. Rectangle · A rectangle's opposite sides are always parallel. Triangles only have three sides, so they can't have two pairs.
  4. True · A square's opposite sides are parallel, and each corner is a right angle, so neighboring sides are perpendicular too.
  5. 8 · 2 x 4 = 8 right angles.
  6. Yes, because one angle is 90 degrees · A right triangle only needs one 90-degree angle. The other two angles can be any size, as long as all three add up correctly.
  7. Sides 3, 4, 5 · 3, 4, 5 satisfies 3² + 4² = 5².
  8. False · Ben is wrong: two right angles already use 180 degrees.
  9. No, a right triangle has perpendicular sides but no parallel sides · A right triangle's two legs meet at a right angle, so they are perpendicular. But none of its three sides run parallel to each other.
  10. 8 · 4 + 4 = 8 right angles.
Worksheet · LightMySky