Question

(b) In the given figure, D is mid point of side AB of A ABC and BDEC is a parallelogram
Prove that Area of A ABC = Area of ||gm BDEC.​

Answer 1

Answer:

Step-by-step explanation:

D is the midpoint of side AB

i.e. AD=BD

Since BDEC is a ║gm

FD║ BC

Therefore, F is the midpoint of AC (mid point theorem)

i.e. AF=CF ......(1)

Now, consider parallel lines ED and BC, with transversal AB

∠DBC = ∠ADE (corresponding angles)

∠CED = ∠DBC (opp. angles are equal)

Therefore, ∠CED =∠ADE......(2)

Now, consider triangles CEF and ADF,

CF=AF (equation 1)

∠CED =∠ADE (equation 2)

∠CFE=∠AFD (vertically opp. angles)

ΔCFE≅ΔAFD (AAS)

therefore, ar(CFE) =ar(AFD)

then, ar(CFE) + ar(BCFD)= ar(AFD)+ar(BCFD)

i.e. ar(BDEC) =ar(ABC)

Hence Proven

Answer 2

Answer:

hope it helps you a lot

Step-by-step explanation:

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