Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

Diagonals AC , BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) =ar (BOC).
Asked by | 13 Sep, 2008, 04:12: PM
answered-by-expert Expert Answer

Denote

the Area (triangle AOD) as Area(I)

The Area (triangle BOC ) as Area(II)

Area (triangle AOB) as Area(III)

Given that

Area(I)=Area(II)

So,

Area(I)+Area(III)=Area(II)+Area(III)

This gives us that,

Area(triangle ADB)=Area(triangle ACB)

So, AB must be parallel to DC ..(as triangles on the same base and equal in area must lie between same parallels)

So, ABCD is a trapezium as one pair of opposite sides is parallel.

 

Answered by | 22 Jan, 2009, 01:45: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
area of right triangle is 240cm and side other than hypotenuse is 30cm.find the perimeter
Asked by bascaljoseph | 07 Feb, 2023, 01:27: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
find the perimeter of a square field whose area is 13689 metre square
Asked by yadavPriy000 | 06 May, 2021, 07:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
length of median of an equilateral triangle is 3 cm each side of triangle is
Asked by manugaur698 | 11 Sep, 2020, 04:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
find the percentage increase in the area of the triangle if it side is doubled
Asked by deepakumaraiya200 | 30 Jun, 2020, 09:51: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
how the two parallelograms are equal
Asked by maddinenianr | 21 Mar, 2020, 03:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
ABCD is a quadrilateral.P and Q are the mid points of sides CD and AB respectively.AP and DQ meet at X whereas BP and CQ meet at Y.Prove that area of triangle ADX + area of triangle BCY = area of quadrilateral PXQY.
Asked by abhishema7 | 19 Jan, 2020, 12:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Area, base and corresponding altitude are x2, x-3 and x+4 respectively. Find the area of parallelogram.
Asked by prakash.sanyasi | 04 Jan, 2020, 05:09: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
an isosceles right angled triangle has an area of 8cm square.find the lenght of its hypotenuse.
Asked by kishor.kp14 | 15 Dec, 2019, 05:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
The sides of a triangular plot are in the ratio of 3:5:7 and it's perimeter is300 meter .find its area
Asked by ravinderchoudhary0486 | 06 Dec, 2019, 10:59: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
prove that parallelograms on the same base and with same area lie between the same parallels
Asked by suresh | 27 Nov, 2019, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×