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Standard X
Maths
Basic Proportionality Theorem (Thales Theorem)
Question

$$D$$ and $$E$$ are points on the sides $$AB$$ and $$AC$$ respectively of a $$\Delta ABC$$ such that $$DE || BC$$. Find the value of $$x$$, when $$AD = 4 \text{ cm}, DB = (x - 4) \text{ cm}, AE = 8 \text{ cm}$$ and $$EC = (3x - 19) \text{ cm}$$.

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Solution
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Given : $$AD = 4 \text{ cm}, DB = (x - 4) \text{ cm}, AE = 8 \text{ cm}$$ and $$EC = (3x - 19) \text{ cm}$$.

To Find : $$x$$

We know that, by BPT(Basic proportionality theorem)

$$\dfrac{AD}{DB} = \dfrac{AE}{EC}$$
$$\dfrac{4}{(x-4)} = \dfrac{8}{(3x-19)}$$

$$ 4(3x-19) = 8(x-4)$$

$$12x-76=8x-32$$
Solving, we get $$x = 11 \text{ cm}$$

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Q1

D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC
Find the value of x, when

(i) AD = x cm, DB = (x - 2) cm,

AE = (x + 2) cm and EC = (x - 1) cm.

(ii) AD = 4 cm, DB = (x - 4) cm, AE = 8 cm and EC = (3x - 19) cm.

(iii) AD = (7x - 4) cm, AE = (5x - 2) cm, DB = (3x + 4 ) cm and EC = 3x cm.

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Q2
In a ΔABC, D and E are points on the sides AB and AC respectively such that DE||BC.
If AD=4 cm,DB=4.5 , and AE=8 cm, find AC.
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Q3
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Q4
State true or false:
In ΔABC, D and E are the points on sides AB and AC respectively. If AB=9cm,AD=4cm,AE=6cm and EC=7.5cm, then DE∥BC.

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Q5
In a ΔABC, D and E are points on the sides AB and AC respectively such that DE||BC.
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