Squares, rectangles and how to build them. Read a little, then play. Clear all six games!
What it is
A rectangle is a four sided shape with four right angles (90 degrees) and opposite sides equal. A square is a special rectangle where all four sides are equal.
Why it works
Both have four square corners. The only difference is that a square has all sides the same length, while a rectangle only needs its opposite sides equal. So every square is a rectangle, but not every rectangle is a square.
Why it matters
We see squares and rectangles everywhere, in tiles, doors, books and screens, so knowing them helps in design and building.
A few examples
A shape with sides 5, 5, 5, 5 is a square. A shape with sides 6, 3, 6, 3 is a rectangle.
What it is
A diagonal joins two opposite corners. A square and a rectangle each have two diagonals.
Why it works
The diagonals of a rectangle are always equal in length and cut each other exactly in half. In a square they are equal AND meet at right angles, because of its extra symmetry.
Why it matters
Diagonals help us check a shape is built correctly, builders measure both diagonals to make sure a frame is truly rectangular.
A few examples
In a rectangle both diagonals are equal. In a square they are equal and cross at 90 degrees.
What it is
To tell a square from a rectangle, look at the side lengths: all four equal means a square, only opposite sides equal means a rectangle.
Why it works
The corners are right angles in both, so the sides are what decide it. If length equals breadth it is a square, otherwise it is a rectangle.
Why it matters
Sorting shapes by their properties is the start of geometry and of clear thinking.
A few examples
4 by 4 is a square. 5 by 3 is a rectangle.
What it is
The points that are the same distance from two points A and B all lie on one straight line, exactly midway between them, called the perpendicular bisector.
Why it works
If a point is the same distance from A and from B, it must sit on the line of symmetry between them. The exact halfway point on the segment AB is the midpoint.
Why it matters
This idea helps place something fairly between two spots, like a lamp equally far from two houses.
A few examples
The midpoint of 2 and 8 on a line is 5. Every point on the perpendicular bisector is equally far from A and B.
What it is
A rectangle: opposite sides equal, all four angles 90 degrees, two equal diagonals. A square: all sides equal, all angles 90 degrees, diagonals equal and at right angles.
Why it works
These properties come straight from the definitions and never change, so we can use them to check or build a shape without measuring everything.
Why it matters
Knowing the properties lets you spot a correct shape at a glance.
A few examples
In a rectangle opposite sides are equal. In a square all sides are equal.
What it is
To construct a square or rectangle we use a ruler for straight equal lengths and a set square or compass to make the corners exact right angles.
Why it works
You start with one side of the correct length, then draw right angles at its ends and mark off the other sides equal, so the shape closes up perfectly.
Why it matters
Careful construction is how we make accurate drawings, plans and designs.
A few examples
For a square of side 5 cm, first draw a 5 cm line. Then make a right angle at each end.
Have a go on paper first, then tap to see the clear steps.
Q1. A shape has sides 7, 7, 7 and 7 with four right angles. What is it?
Q2. A shape has sides 8, 4, 8 and 4 with four right angles. What is it?
Q3. How many diagonals does a rectangle have, and are they equal?
Q4. On a number line, what is the midpoint of 4 and 10?
Q5. In a rectangle, every angle measures how many degrees?
Q6. To construct a square of side 6 cm, what length is the first line you draw?