# When is a rectangle not a square and why?

## When is a rectangle not a square and why?

If they are of equal length, then THAT RECTANGLE IS A SQUARE. If the rectangle’s 2 pairs of parallel sides are not of equal length then THAT RECTANGLE IS NOT A SQUARE. So, to conclude: A RECTANGLE MAY OR MAY NOT BE A SQUARE, [ie, ALL SQUARES ARE RECTANGLES. SOME RECTANGLES ARE SQUARES.]

When is a square a rectangle or a parallelogram?

A [&square&] is also a parallelogram whose sides intersect at 90° angles. Therefore, like a rectangle its opposite sides are congruent. However, a [&square&] has an added feature. It is also a rhombus. Therefore, all of its sides are congruent. A rectangle is a [&square&] when both pairs of opposite sides are the same length.

Which is a special case of a rectangle?

A rectangle is a quadrilateral, all of whose angles are equal i.e. right angles. Square, apart from all equal angles, also has all sides equal. Hence, square is a special case of rectangle. In other words rectangle is sometimes a square (when all sides too are equal).

### When does a square maximize the area of a rectangle?

The only time this isn’t possible is when all of the sides are the same length — that is, when the rectangle is a square. Therefore, a square maximizes area for a given perimeter. Let R be a rectange with sides x, y s.t x + y = k, k ∈ N fixed, let us find the maximum of f ( x, y) := x y:

Why is a square always a regular polygon?

Explanation: A regular polygon is both equilateral (all sides are the same length) and equiangular (all angles are the same measure). A square perfectly matches this description. A square’s four sides must all be the same length and a square must have four angles measuring 90˚ by definition. For example, take the picture below.

What is the same about a rectangle and square?

A rectangle is a square when both pairs of opposite sides are the same length . This means that a square is a specialized case of the rectangle and is indeed a rectangle.

#### Is a square always a rectangle?

Every square is a rectangle, but not every rectangle is a square. A rectangle always has 4 right angles. So does a square, so that can be considered a rectangle. A rectangle can have sides of any length just as long as all four angles are right angles. A square however must have congruent sides.

Why are all squares consider rectangles?

So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.