In the given figure, ABCD is a parallelogram. AE divides the line

Q) In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1:2. If BE = 1.5 cm, then find the length of BC.

Ans: Since AD ǁ BC, and EA cuts these lines,

$\therefore$ ∠DAE = ∠AEB or (∠OEB)

Similarly, Line DB cuts these parallel lines,

$\therefore$ ∠ADB = ∠DBC or (∠OBE)

Therefore, Δ AOD ~ Δ BOE

Hence, $\frac{BE}{AD} = \frac{OB}{OD}$ ………….. (i)

Given that AE divides the line segment BD in the ratio 1:2

Hence, $\frac{OB}{OD} = \frac{1}{2}$ …………. (ii)

Comparing equations (i) and (ii), we get, $\frac{BE}{AD} = \frac{1}{2}$

Given that BE = 1.5 cm

$\therefore$ AD = 3 cm

Since, ABCD is a parallelogram

$\therefore$ BC = AD = 3 cm

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