Home
Class 9
MATHS
Show that the diagonals of a parallelog...

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

Text Solution

Verified by Experts

P is mid point of AC and BD
AP=PC
PB=DP
`/_APB and /_DPC`
AP=PC
PB=PD
AB=DC
area of `/_APB`=area of `/_DPC`
...
Promotional Banner

Topper's Solved these Questions

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    NCERT|Exercise Solved Examples|4 Videos
  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    NCERT|Exercise Exercise 9.2|6 Videos
  • CIRCLES

    NCERT|Exercise EXERCISE 10.2|2 Videos

Similar Questions

Explore conceptually related problems

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

A diagonal of a parallelogram divides it into two congruent triangles.

A diagonal of a parallelogram divides it into two triangles of equal area. GIVEN : A parallelogram A B C D in which B D is one of the diagonals. TO PROVE : ar ( A B D)=a r( C D B)

Show that each diagonal of a parallelogram divide it into two congruent triangles. The following are the steps involved in showing the above result. Arrange them in sequential order. A) In triangleABC and triangleCDA , AB=DC and BC=AD (therefore opposite angles of parallelogram) AC=AC (common side). B) Let ABCD be a parallelogram. Join AC. C) By SSS congruence property, triangleABC ~=triangleCDA . D) Similarly, BD divides the triangle into two congruent triangles.

A diagonal of parallelogram divides it into two congruent triangles.

The diagonals of a parallelograms are equal .

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

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

Asserion (A) : The diagonals of a ||gm divide it into four triangle of equal area. Reason (R ) : A diagonal of a ||gm divides it into two triangle of equal area.