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primary 6 | Maths
| Geometry

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Pls help to explain

A random four sided figure is nameless.

Have two sides being parallel to each other and you call the new shape a trapezium.

Have two sets of opposite sides being parallel and equal in length and you have a parallelogram.

If the parallelogram has all four angles being 90 degrees, it is called a rectangle.

If the parallelogram has all four sides equal in length, it is called a rhombus.

If the rectangle has all four sides being equal, it is called a square.

If the rhombus has all four angles being 90 degrees, it is called a square.

A square can therefore also be called as the following.

1. A rhombus with all four angles being 90 degrees.

2. A rectangle with all four lengths equal.

3. A parallelogram with all four sides being equal and all four lengths being 90 degrees

And so on.

For option (3), notice that opposite sides are parallel and equal in length, but adjacent sides are not equal.

The top right and bottom left sides are obtained by moving 1 unit horizontally and 2 units vertically on the grid.

The top left and bottom right sides are obtained by moving 2 units horizontally and 2 units vertically on the grid.

So this figure is actually a parallelogram

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For option 2, we know that it's a rectangle, so it's wrong too.

The problem comes with (3) and (4) is because this question is also testing us whether we read the square grid carefully and our concept of rhombus.

To see clearly, the breadth of the shape(parallelogram) is not equal to the length. Therefore, since (4) has 4 equal sides which is a square, (4) would be the right answer.