Questions & Answers

Question

Answers

All rhombuses are kites.

a)True

b)False

c)Ambiguous

d)Data Insufficient

Answer
Verified

Hint: First write down all the properties of both the quadrilaterals then try to focus on common ones for which you can say about the statement.

Complete step-by-step answer:

In the question, we are asked about whether all rhombuses are kites is true or false.

Before just writing let’s write briefly what are the characteristics of rhombus and kites.

A quadrilateral is a rhombus if any of the following satisfy.

A parallelogram in which diagonals bisect interior angle.

A parallelogram in which any two consecutive or adjacent sides are equal.

A parallelogram in which diagonals are perpendicular to each other and bisect too.

A quadrilateral in which four sides are equal.

A quadrilateral is a kite if any of the following satisfy:

Two disjoint pairs of adjacent sides are equal.

One diagonal is the perpendicular bisector of the other diagonal.

One diagonal is a line of symmetry.

One diagonal bisects a pair of opposite angles.

So, in analysis we can say that a kite is a quadrilateral whose four sides can be grouped into two pairs of equal length sides that are adjacent to each other and only pairs of opposite angles are equal. All sides of rhombus are equal and opposite angles are equal.

So, the correct option is ‘A’.

Note: We can also say that in general, any quadrilateral with perpendicular diagonals one of which is line of symmetry is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is rhombus.

Complete step-by-step answer:

In the question, we are asked about whether all rhombuses are kites is true or false.

Before just writing let’s write briefly what are the characteristics of rhombus and kites.

A quadrilateral is a rhombus if any of the following satisfy.

A parallelogram in which diagonals bisect interior angle.

A parallelogram in which any two consecutive or adjacent sides are equal.

A parallelogram in which diagonals are perpendicular to each other and bisect too.

A quadrilateral in which four sides are equal.

A quadrilateral is a kite if any of the following satisfy:

Two disjoint pairs of adjacent sides are equal.

One diagonal is the perpendicular bisector of the other diagonal.

One diagonal is a line of symmetry.

One diagonal bisects a pair of opposite angles.

So, in analysis we can say that a kite is a quadrilateral whose four sides can be grouped into two pairs of equal length sides that are adjacent to each other and only pairs of opposite angles are equal. All sides of rhombus are equal and opposite angles are equal.

So, the correct option is ‘A’.

Note: We can also say that in general, any quadrilateral with perpendicular diagonals one of which is line of symmetry is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is rhombus.

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