Question

in angle ABC,D AND E are the mid point of sidesAB and AC respectivly.show that ar angle ADE=1/4 ar angle ABC.

Answer 1

By using converse of mid-point theorem,we get DE is parallel to BC. That implies angleADE =angleDBC and angleAED=angleECB(since corresponding angles are equal). By using A.A.axiom we get triangle ADE is similar to triangle ABC. Then ratio of AE^2&AC^2=area of triangleADE ÷area of triangleABE. As ratio of AE^2&AC^2=1^2÷2^2=1÷4. That implies ar(ADE)÷ar(ABC)=1÷4. That implies ar(ADE)=ar(ABE)(1÷4)