Two triangles on the same base (or equal bases) and between the same parallels are equal in area Now, suppose ABCD is a parallelogram whose one of the diagonals is AC
(see Fig. 9.20). Let AN ⊥ DC. Note that
` /_\ ADC ~= /_\ CBA` (Why?)

So,` ar (ADC) = ar (CBA)` (Why?)

Therefore, `ar (ADC) = 1//2 ar (ABCD) = 1//2 (DCxx AN)` (Why?)

So, area of `/_\ ADC` = 1/2 `xx base DC xx` corresponding altitude `AN`.
Dusre shabdo mei, area of a triangle is half the product of its base (or any side) and the corresponding altitude (or height). Aapko yaad hoga area of triangle ka formula Class VII ? From this formula, two triangles with same base (or equal bases) and equal areas hai toh unke corresponding altitudes equal honge. Iss result se ek theorem aati hai.

Explanation

Two triangles on the same base (or equal bases) and between the same parallels are equal in area
Now, suppose ABCD is a parallelogram whose one of the diagonals is AC

(see Fig. 9.20). Let AN ⊥ DC. Note that
/_\ ADC ~= /_\ CBA (Why?)
So, ar (ADC) = ar (CBA) (Why?)
Therefore, ar (ADC) = 1/2 ar (ABCD) = 1/2 (DC AN) (Why?)
So, area of /_\ ADC = 1/2 × base DC × corresponding altitude AN
Dusre shabdo mei, area of a triangle is half the product of its base (or any side) and the corresponding altitude (or height). Aapko yaad hoga area of triangle ka formula Class VII ? From this formula, two triangles with same base (or equal bases) and equal areas hai toh unke corresponding altitudes equal honge.
Iss result se ek theorem aati hai.