Question

In fig.9.33, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that

(i) ar(BDE)= 1/4 ar(ABC)
(ii) ar(BDE)=1/2 ar(BAE)
(iii) ar (ABC)= 2 ar (BEC)
(iv) ar(BFE) = ar (AFD)
(v) ar(BFE)= 2ar (FED)
(vi) ar (FED)= 1/8 ar (AFC)

[ Hint: join EC and AD. show that BE||AC and DE||AB,etc.]​

Answer 1

In fig.9.33, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that

(i) ar(BDE)= 1/4 ar(ABC)

(ii) ar(BDE)=1/2 ar(BAE)

(iii) ar (ABC)= 2 ar (BEC)

(iv) ar(BFE) = ar (AFD)

(v) ar(BFE)= 2ar (FED)

(vi) ar (FED)= 1/8 ar (AFC)

[ Hint: join EC and AD. show that BE||AC and DE||AB,etc.]

Answer 2

Answer:

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Step-by-step explanation:

(i) ar(BDE)= 1/4 ar(ABC)

(ii) ar(BDE)=1/2 ar(BAE)

(iii) ar (ABC)= 2 ar (BEC)

(iv) ar(BFE) = ar (AFD)

(v) ar(BFE)= 2ar (FED)

(vi) ar (FED)= 1/8 ar (AFC)

[ Hint: join EC and AD. show that BE||AC and DE||AB,etc.]