Can a rhombus be a trapezoid?

Answer

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Hint: In this question, we need to check whether a rhombus can be a trapezoid . Generally, Rhombus and trapezoid are quadrilaterals. A quadrilateral is nothing but a polygon with four sides . With the help of the definition and properties of these two quadrilaterals , we can compare the properties of both quadrilaterals. From that we can check if a rhombus can be a trapezoid .So, we can proceed with our solution as follows.

Complete step-by-step answer:

First let us know the definition of rhombus and trapezoid.

Mathematically, there are seven types of quadrilaterals. Rhombus and trapezoid are one among the types of quadrilaterals.

Rhombus :

Rhombus is a quadrilateral with four congruent sides. The plural of rhombus is known as rhombi. A rhombus usually has all the properties of a parallelogram.

Trapezoid :

A quadrilateral with exactly one pair of parallel sides is called trapezoid. The parallel sides are generally referred to as bases.

Now let us compare the properties of rhombus and trapezoid.

1.Moreover, opposite sides of rhombus are parallel whereas only one pair of opposite sides of trapezoid is parallel and all the four sides are not equal.

2. All the four sides of the rhombus are equal but in trapezoid parallel sides are not equal.

3. The special form of rhombus is square where all the four angles of the rhombus are right angles whereas in trapezoid two pairs of adjacent angles are obtuse and acute.

4. The opposite angles are equal in rhombus but in trapezoid the opposite angles are not equal.

5. In rhombus, four pairs of adjacent angles are supplementary but in trapezoid only two pairs of adjacent angles are supplementary.

Thus from these points we can conclude that the rhombus can never be a trapezoid.

Final answer :

The rhombus can never be a trapezoid.

Note: We may have some confusion with the word trapezoid and trapezium depending on which country we’re in. In India and Britain, they usually say trapezoid but in America, they usually say trapezium, trapezium means a quadrilateral with no parallel sides. But also a rhombus is a special type of trapezoid with some similarities . Some of the similarities are that both are geometrically convex quadrilaterals , Both have four sides and four angles and both have the sum of their interior and the exterior angles as \[360^{o}\] .

Complete step-by-step answer:

First let us know the definition of rhombus and trapezoid.

Mathematically, there are seven types of quadrilaterals. Rhombus and trapezoid are one among the types of quadrilaterals.

Rhombus :

Rhombus is a quadrilateral with four congruent sides. The plural of rhombus is known as rhombi. A rhombus usually has all the properties of a parallelogram.

Trapezoid :

A quadrilateral with exactly one pair of parallel sides is called trapezoid. The parallel sides are generally referred to as bases.

Now let us compare the properties of rhombus and trapezoid.

1.Moreover, opposite sides of rhombus are parallel whereas only one pair of opposite sides of trapezoid is parallel and all the four sides are not equal.

2. All the four sides of the rhombus are equal but in trapezoid parallel sides are not equal.

3. The special form of rhombus is square where all the four angles of the rhombus are right angles whereas in trapezoid two pairs of adjacent angles are obtuse and acute.

4. The opposite angles are equal in rhombus but in trapezoid the opposite angles are not equal.

5. In rhombus, four pairs of adjacent angles are supplementary but in trapezoid only two pairs of adjacent angles are supplementary.

Thus from these points we can conclude that the rhombus can never be a trapezoid.

Final answer :

The rhombus can never be a trapezoid.

Note: We may have some confusion with the word trapezoid and trapezium depending on which country we’re in. In India and Britain, they usually say trapezoid but in America, they usually say trapezium, trapezium means a quadrilateral with no parallel sides. But also a rhombus is a special type of trapezoid with some similarities . Some of the similarities are that both are geometrically convex quadrilaterals , Both have four sides and four angles and both have the sum of their interior and the exterior angles as \[360^{o}\] .

Last updated date: 06th Sep 2023

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