Question

if ABCD is a parrallelogram then prove that; ar.triangle ABD = ar triangle BCD=ar .triangleABC = ar triangle ACD =1/2 ar //gm ABCD​

Answer 1

Answer:

Step-by-step explanation: In ║gm ABCD and ΔABD

Common Base = ab and ab║ cd

∴ ar Δ abd = 1/2 ar ║gm abcd (if a triangle and a parallelogram are on the same base and between same parallels then the area of triangle is 1/2 the area of the parallelogram)        -- (1)

In ║gm ABCD and ΔBCD

Common Base = bc and ad║bc

∴ ar Δ bcd = 1/2 ar ║gm abcd  --(2)

In ║gm ABCD and ΔABC

Common Base = ab and ab║ cd

∴ ar Δ abc = 1/2 ar ║gm abcd --(3)

In ║gm ABCD and ΔACD

Common Base = dc and ab║ cd

∴ ar Δ acd = 1/2 ar ║gm abcd --(4)

∴From 1,2,3 and 4

ar Δabd = ar Δbcd = ar Δabc = ar Δacd =  1/2 ar ║gm abcd

Answer 2

hey mate

This is your answer

thanks

regards

aditya