6.2 Basic Proportionality Theorem (Thales Theorem)

Key Formulas

Solved Examples

Step 1

Since $DE || BC$ , we apply the Basic Proportionality Theorem.

Step 2

Formula: $\frac{AD}{DB} = \frac{AE}{EC}$ .

Step 3

Substitute values: $\frac{1.5}{3} = \frac{1}{EC}$ .

Step 4

Simplify LHS: $\frac{1.5}{3} = \frac{1}{2}$ .

Step 5

So, $\frac{1}{2} = \frac{1}{EC} \implies EC = 2$ cm.

Final Answer

2 cm

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