Question

How can you use properties of rhombus, rectangles, and squares to solve problems? How does a square relate to a rectangle and rhombus?

Answer 1

Rhombus, rectangles, and squares have specific properties that can be used to solve problems in geometry. These properties include perimeter, area, and diagonals. A square is a special type of rectangle and rhombus, combining the properties of both shapes.

Step-by-step explanation:

Rhombus, rectangles, and squares are all quadrilaterals with specific properties that can be used to solve problems in geometry. Here are a few examples of how these properties can be applied:

1. Perimeter: The perimeter of a rhombus, rectangle, and square can all be found by adding up the lengths of their sides. This can be useful in finding the total length of fencing needed for a given shape.
2. Area: The area of a rectangle and square can be found by multiplying the length and width of the shape. For a square, since all sides are equal, the formula simplifies to side length squared. This can be helpful in finding the amount of space inside a given shape.
3. Diagonals: The diagonals of a rhombus, rectangle, and square have specific relationships. In a square, the diagonals are congruent and bisect each other. In a rectangle, the diagonals are not congruent but bisect each other. In a rhombus, the diagonals are not congruent and do not bisect each other.

In terms of how squares relate to rectangles and rhombuses, a square is a special type of rectangle where all sides are equal, and it is also a special type of rhombus where all angles are right angles. So, a square has properties of both a rectangle and a rhombus.

Answer 2

Given:

Rhombus, rectangle and square.

Required:

How properties of rhombus, rectangle and square are used to solve problems and how does a square relate to a rectangle and rhombus.

Answer:

We know that the the opposite sides of square, rectangle and rhombus are parallel to each other.

The diagonals of square and rhombus are perpendicular bisectors of each other, whereas the diagonals of rectangle are only bisector of each other.

All sides of rhombus and square are of equal length, but in rectangle only opposite sides are of equal length.

All the interior angles of the square and rectangle are right angle and in case of rhombus, opposite angles are of same measure.

Using these properties of rhombus, rectangle and square, we can solve any problem regarding sides, angles and diagonals.

A square relate to a rectangle and rhombus in respect of the diagonals such that diagonals in these three are bisectors of each other.