This essay will compare and contrast the rhombus, rectangle, and square. It will provide definitions for each quadrilateral and discuss their shared and unique characteristics.
A rhombus is defined by its congruent opposite sides and angles, as well as supplementary consecutive angles. Additionally, its diagonals bisect each other.
In contrast, a rectangle has congruent angles and diagonals.
Lastly, a square is characterized by having all right angles and interior angles that always add up to 360 degrees.
Both the square and the rectangle are types of quadrilaterals, each with their own distinct characteristics. A square is unique because all four of its sides are congruent, while a rectangle does not necessarily have congruent sides. The trapezoid, kite, and rhombus also fall into this category of quadrilaterals.
A rhombus is a specific type of parallelogram where all four sides are congruent. This fact is explained in the rhombus corollary, which states that a quadrilateral can only be considered a rhombus if it has four congruent sides.
Similarly, a rectangle is another kind of parallelogram but with four equal angles instead of sides. According to the rectangle corollary, a rectangle can be classified as a rhombus only if it has four congruent sides.
Lastly, a square is also categorized as a parallelogram but possesses both four equal angles and sides. The square corollary asserts that for any quadrilateral to qualify as a square, it must have both four congruent angles and sides.
These three quadrilaterals share similarities as they are all parallelograms with four sides where opposite sides are parallel. Their diagonals also intersect at the midpoint. However, there are differences among them. For instance, a square has congruent angles and sides, while a rhombus only has congruent sides. In summary, I have discussed the distinctions between a rhombus, rectangle, and square along with definitions for each. Lastly, I have described how these three quadrilaterals…