Track quiz

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
Idea	How it goes
Four sides	Straight sides, a closed path, and no side cutting through another.
Corner total	Cut it along a diagonal that lies inside it. The four angles total exactly 360°.
Diagonals	A line to a corner that is not a neighbour. Count them as n × (n − 3) ÷ 2.
Trapezium	At least one pair of parallel sides.
Parallelogram	Both pairs of opposite sides parallel. Sides match, angles match, neighbours make 180°.
Rectangle	Both pairs parallel, and all four corners exactly 90°.
Rhombus	Both pairs parallel, and all four sides the same length.
Halving	A parallelogram's diagonals cut each other in half. Equal length is a separate ask.
The two extras	A rectangle's diagonals match in length. A rhombus's cross at exactly 90°.
Several names	Every 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.

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