Question

in the figure given below, ABC and DBC are two triangles on the same base BC. if AD is intersect BC at O then show that :ar(ABC)/ar(DBC) = AO/DO

Answer 1

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please refer to the attachment above..

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Answer 2

Area of ΔABC/Area of ΔDBC   = AO/DO

Step-by-step explanation:

ABC and DBC are two triangles on the same base BC

AD is intersect BC at O

Lets draw AP⊥BC   & DQ⊥BC

Area of ΔABC = (1/2)BC * AP

Area of ΔDBC = (1/2)BC * DQ

ΔAOP & ΔDOQ

∠AOP = ∠DOQ ( opposite angles)

∠APO = ∠DQO  = 90°

=> ΔAOP ≈ ΔDOQ

=> AP/DQ = AO/DO = PO/QO

Area of ΔABC/Area of ΔDBC   =  ((1/2)BC * AP)  / ((1/2)BC * DQ)

= AP/DQ

= AO/DO

Area of ΔABC/Area of ΔDBC   = AO/DO

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