Home
Class 9
MATHS
If each diagonals of a quadrilateral ...

If each diagonals of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram.

Text Solution

AI Generated Solution

To prove that a quadrilateral is a parallelogram if each diagonal separates it into two triangles of equal area, we can follow these steps: ### Step-by-Step Solution: 1. **Define the Quadrilateral and Diagonals**: Let quadrilateral ABCD have diagonals AC and BD. We are given that diagonal AC divides the quadrilateral into two triangles, ABC and ACD, with equal areas. 2. **Area of Triangles from Diagonal AC**: ...
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/exemplar|12 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|34 Videos

  • CIRCLE

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (long Answer Questions )|5 Videos

Similar Questions

Explore conceptually related problems

If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D are such that a r( A B D)=a r( C D B ) and a r( A B C)=a r( A C D)dot TO PROVE: Quadrilateral A B C D is a parallelogram.

Prove that A diagonal of a parallelogram divides it into two triangles of equal area.

Show that a median of a triangle divides it into two triangles of equal areas.

Show that a median of a triangle divides it into two triangles of equal area.

If the diagonals A C ,\ B D of a quadrilateral A B C D , intersect at O , and separate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram.

If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O , and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D intersect at O and separate it into four parts such that a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D) TO PROVE : Quadrilateral A B C D is a parallelogram.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

The diagonal AC of a quadrilateral ABCD divides it into two triangles of equal areas. Prove that diagonal AC bisects the diagonal BD.