If the ratio of sides -taken in order- of a quadrilateral is a-b-b-a- then it is a nbsp- cyclic quadrilateral-parallelogram-square-kite-

The correct option is D kite Here, the ratio is given to be a:b:b:a. If KLMJ nbsp;is a quadrilateral, the sides are in the ratio a:b:b:a. Let KL nbsp;= a, ...

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Byju's Answer

Standard IX

Mathematics

Kite

If the ratio ...

Question

If the ratio of sides (taken in order) of a quadrilateral is a:b:b:a, then it is a

kite

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cyclic quadrilateral

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parallelogram

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square

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Solution

The correct option is A
kite

Here, the ratio is given to be a:b:b:a.
If KLMJ is a quadrilateral, the sides are in the ratio a:b:b:a.

Let KL = a, LM = b, MJ = b and JK = a.

Here, JK and LM are equal and LM and MJ are equal.

We know that, kite is a quadrilateral with two pairs of adjacent sides equal in length.

The data given implies that we have two disjoint pairs of adjacent sides which are equal i.e. there are two pairs of adjacent sides which are equal and the opposite sides are not equal.

This is the very definition of a kite.

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Similar questions

If $∠ A, ∠ B, ∠ C a n d ∠ D$ of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a

(a) rhombus

(b) kite

(d) parallelogram

Q. Complete each of the following statements by means of one of those given in brackets against each:
(i) If one pair of opposite sides are equal and parallel, then the figure is ........................
(parallelogram, rectangle, trapezium)

(ii) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................ (square, rectangle, trapezium)

(iii) A line drawn from the mid-point of one side of a triangle .............. another side intersects the third side at its mid-point. (perpendicular to parallel to, to meet)

(iv) If one angle of a parallelogram is a right angle, then it is necessarily a .................
(rectangle, square, rhombus)

(v) Consecutive angles of a parallelogram are ...................
(supplementary, complementary)

(vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ...............
(rectangle, parallelogram, rhombus)

(vii) If opposite angles of a quadrilateral are equal, then it is necessarily a ....................
(parallelogram, rhombus, rectangle)

(viii) If consecutive sides of a parallelogram are equal, then it is necessarily a ..................
(kite, rhombus, square)

Q. A quadrilateral whose opposite sides are parallel is called
(a) rhombus
(b) a kite
(c) a trapezium
(d) a parallelogram

Complete each of the following statements by means of one of those given in brackets against each :

(i) If one pair of opposite sides is equal and parallel, then the figure is ........

(parallelogram, rectangle, trapezium)

(ii) If in a quadrilateral only one pair of opposite sides is parallel, the quadrilateral is .......

(square, rectangle, trapezium)

(iii) A line is drawn from the mid-point of one side of a triangle ......, another side intersects the third side at its mid-point.

(perpendicular to, parallel to, to meet)

(iv) If one angle of a parallelogram is a right angle, then it is necessarily a ......

(rectangle, square, rhombus)

(v) The consecutive angle of a parallelogram is......

(supplementary, complementary)

(vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ........

(rectangle, parallelogram, rhombus)

(vii) If opposite angles of a quadrilateral are equal, then it is necessarily a ...........

(parallelogram, rhombus, rectangle)

(viii) If consecutive sides of a parallelogram are equal, then it is necessarily a ..........

(kite, rhombus, square)

Q. A quadrilateral having all sides equal is a

(a) square
(b) parallelogram
(c) rhombus
(d) kite

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