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655-705 Level|   Geometry|      
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Bunuel
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Is ABCD rectangular 05 Mar 2021, 09:25
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ravish844
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can you list the useful properties of kite. In GMATCLUB MATHBOOK also i have searched but am not able to get the properties of kite

Kite is a quadrilateral with two distinct pairs of equal adjacent sides:
Attachment:
Kite.gif

Properties of a kite
Diagonals intersect at right angles.

Angles between unequal sides are equal
In the figure above notice that ∠BAC = ∠BCD no matter how how you reshape the kite.

Area
The area of a kite is half the product of the diagonals: \(area=\frac{d_1*d_2}{2}\)

A kite can become a rhombus
In the special case where all 4 sides are the same length, the kite satisfies the definition of a rhombus. A rhombus in turn can become a square if its interior angles are 90°.

Hope it helps.


Hi Bunuel,

Here, you mean ∠BAD = ∠BCD, I believe.
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Right. Edited the typo. Thank you!
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Is ABCD rectangular 05 Mar 2021, 21:22
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Bunuel
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Is ABCD rectangular?
1). Angle ABC and BCD are right angle
2). Two diagonal have the same length.

only square and rectangle can have equal diagonals. All squares are rectangles .SO option B is sufficient. Can some one shed light on this?

That's not true. For example, consider isosceles trapezoid or kite with equal diagonals.
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Hi Bunuel,

I can understand the case of isosceles trapezoid/trapezium having equal diagonals.

However I'm having confusion with "kite with equal diagonals".
Wouldn't a kite having equal diagonals be a special case of rhombus having equal diagonals or more specifically a square?
This is because a kite having equal diagonals would have all sides equal. It is not the usual kite as per definition, where we have two distinct pairs of equal sides.
I tried to draw this as well, but using Pythagoras theorem, I deduced that all sides are equal.

Or am I missing something here. Please suggest.
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Is ABCD rectangular 05 Feb 2023, 00:14
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