Properties Of Squares And Rectangles
Hello there. This math post is an overview of squares and rectangles with their own properties. Squares and rectangles are popular four-sided shapes (quadrilaterals) which are seen almost everywhere.
Topics
- Rectangles And Its Properties
- Properties Of Squares
- Practice/Knowledge Problems
- Answers To Practice/Knowledge Problems
Rectangles And Its Properties
A rectangle is a four sided closed shape where the opposite pair of sides are of equal length and are parallel. Parallel opposite sides means that the opposite sides do not touch each other if they were to extend (to infinity).
Rectangles have four right angles (90 degrees) where the side lengths next to each other meet at a L shape.
The rectangle is a symmetric shape. You can cut the rectangle into two equal parts. There are two ways to do this. One way is to cut vertically down the middle. The second way is a horizontal cut in the middle of the rectangle.
Even though the opposite pair of sides in a rectangle are of equal length, not all four side lengths in a rectangle are the same. If all four side lengths in the rectangle are the same, that four sided shape is actually a square.
Properties Of Squares
A square is a four sided closed shape where the opposite pair of sides are parallel to each other.
Squares also have four right angles (90 degrees) where the side lengths next to each other meet at a L shape.
Squares and rectangles are quite similar but a square is a special case of a rectangle. A square has all four sides being of equal length while the rectangle may not have all the sides being of equal length.
The square is a also symmetric shape. The rectangle can be cut into two equal parts in two ways but the square has four ways. The ways are vertically down the middle, horizontally in the middle and the diagonals.
Practice/Knowledge Problems
Which shape has all the sides being of equal length? The square or rectangle?
What properties do squares and rectangles share?
How many lines of symmetry does the rectangle have?
How many lines of symmetry does the square have?
Explain how a square is a rectangle but not every rectangle is a square. (Tricky question as it tests communcation skills)
Answers To Practice/Knowledge Problems
Square
Both the rectangle and square has opposite sides being parallel to each other. They both share the fact that they have four sides (quadrilaterals) and have four right angles. Symmetry property is shared with the two shapes.
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A square has all four of its sides being of equal length and also satisfies the rectangle's definition of opposite sides being parallel. Rectangles have opposite sides being equal. The only case where the rectangle is a square if all the sides are of equal length (which would make the rectangle a square).
