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Standard VII

Mathematics

Triangle

If Arjun has ...

Question

If Arjun has a quadrilateral ABCD, how many triangles are there in the quadrilateral such that one of the diagonal forms one of the sides of the triangle?

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Solution

The correct option is D
4

Consider the quadrilateral ABCD above.

The triangles that can be constructed with diagonals as one of the sides are as follows - $△$ ABC, $△$ DBC, $△$ BAD, $△$ CAD.

Hence, 4 triangles are possible.

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Similar questions

If I have a quadrilateral PQRS, how many triangles are there in the quadrilateral in which I must have one of the diagonals as a side.

ABCD is a quadrilateral such that $∠$ ABC $+ ∠$ ADC $= 180^{\circ}$ . Inside the quadrilateral :

Statement 1: the circumcircle of $△$ ABC intersects diagonal BD at D.

Statement 2: the circumcircle of $△$ ABC intersects BD at $D^{^{'}}$ inside the quadrilateral.

Statement 3: the circumcircle of $△$ ABC intersects BD at $D^{^{'}}$ outside the quadrilateral.

Statement 4: the circumcircle of $△$ ABC does not intersect BD at all.

Statement 5: ABCD is called cyclic quadrilateral.

Q. Diagonals

A C

and

B D

of a quadrilateral

A B C D

intersect at

O

in such a way that

a r (△ A O D) = a r (△ B O C)

. Prove that

A B C D

is a trapezium

Q. Diagonals

A C

and

B D

of a quadrilateral

A B C D

interested at

O

in such a way that

a r (△ A O D) = a r (△ B O C)

. Prove that

A B C D

is a trapezium.

ABCD is a convex quadrilateral with 3, 4, 5 and 6 points marked on its sides AB, BC, CD and DA respectively. Triangles are formed using these 18 points and original vertices of the quadrilateral. Number of such triangles that do not have any side or part of a side common with the quadrilateral are

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If Arjun has a quadrilateral ABCD, how many triangles are there in the quadrilateral such that one of the diagonal forms one of the sides of the triangle?

The correct option is D 4 Consider the quadrilateral ABCD above. The triangles that can be constructed with diagonals as one of the sides are as follows - △ABC, △DBC, △BAD, △CAD. Hence, 4 triangles are possible.

The correct option is D
4

Consider the quadrilateral ABCD above.

The triangles that can be constructed with diagonals as one of the sides are as follows - $△$ ABC, $△$ DBC, $△$ BAD, $△$ CAD.

Hence, 4 triangles are possible.