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Lesson 14 of 15

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Ten ideas, ten checks. The table comes first, so nothing has to be remembered cold.

Ten things worth knowing before you name a four-sided shape
IdeaHow it goes
Four sidesStraight sides, a closed path, and no side cutting through another.
Corner totalCut it along a diagonal that lies inside it. The four angles total exactly 360°.
DiagonalsA line to a corner that is not a neighbour. Count them as n × (n − 3) ÷ 2.
TrapeziumAt least one pair of parallel sides.
ParallelogramBoth pairs of opposite sides parallel. Sides match, angles match, neighbours make 180°.
RectangleBoth pairs parallel, and all four corners exactly 90°.
RhombusBoth pairs parallel, and all four sides the same length.
HalvingA parallelogram's diagonals cut each other in half. Equal length is a separate ask.
The two extrasA rectangle's diagonals match in length. A rhombus's cross at exactly 90°.
Several namesEvery square is a rhombus and a rectangle, and both of those are parallelograms.

Four dots are joined into a closed path. One side passes straight through another. What has gone wrong?

  • Nothing — four straight sides is all a quadrilateral needs
  • A quadrilateral also asks that no side cuts through another
  • The dots are in the wrong places and need moving

Three corners of a quadrilateral read 120°, 65° and 100°. What is the fourth?

  • 65°, because the corners come in matching pairs
  • 75°
  • 105°, because the three given add to 255

How many diagonals does a six-cornered shape have?

  • 6, one from each corner
  • 9
  • 15, because there are fifteen pairs of corners

A shape has exactly one pair of parallel sides. Its four sides measure 10, 5, 5 and 4.5. What is its best name?

  • Parallelogram, because a pair of sides is parallel
  • Trapezium
  • Rhombus, because two of its sides are equal

One corner of a parallelogram measures 55°. What are the other three?

  • 55°, 55° and 55°
  • 125°, 55° and 125°
  • 55°, 125° and 125°, in that order round the shape

A parallelogram's diagonals measure 18 and 12. What are the four pieces the crossing makes?

  • 9, 9, 9 and 9
  • 9, 9, 6 and 6
  • 6, 6, 6 and 6

The two diagonals of a parallelogram are exactly the same length. What does that tell you?

  • Its four sides are all equal
  • All four of its corners are exactly 90°. So it is a rectangle
  • Its diagonals cross at exactly 90°

A rhombus has diagonals of 16 and 12. What is the crossing angle, and what are the four pieces?

  • 45°, with pieces of 16, 16, 12 and 12
  • Exactly 90°, with pieces of 8, 8, 6 and 6
  • 60°, with pieces of 8, 8, 6 and 6

Is every rectangle a rhombus?

  • Yes, because both are parallelograms
  • No. A rectangle meets the rhombus list only when its sides are equal
  • No, because a rhombus is never a parallelogram

You have four side lengths and are asked to build the quadrilateral. Why is that not enough?

  • Because a construction always needs an angle
  • Because those four lengths close in more than one way. A fifth measurement picks one
  • Because side lengths cannot be set on a compass

Chapter 4 of Part I is Quadrilaterals. You have dragged a corner. You have ruled both diagonals. You have built a shape from five measurements. See what the chapter asks next.

Next: Number Play. Properties of numbers you already know, checked hard enough to be sure.

Reveal every answer to finish this lesson.