Question

A point d is taken on base bc of a triangle abc and adis produced to e , such that de=ad . Show that ar(bce) = ar (abc )

Answer 1

Answer:

In ACE, since D is the mid-point of AE,

CD is the median

Hence, ar(ADC) = ar(EDC) (1)

Similarly, ar(ADB) = ar(EDB) (2)

Adding (1) and (2),

ar(ADC) + ar(ADB) = ar(EDC) + ar(EDB)

ar(ABC) = ar(BCE)