Question 6

If the line DE is drawn parallel to the base BC of a triangle ABC by intersecting the other two sides, then which of the following is the CORRECT equation for this case.

Solution

Given : DE is parallel to BC

In $$\triangle$$ ABC and $$\triangle$$ ADE,

$$\angle$$ ABC = $$\angle$$ ADE (corresponding angles)

$$\angle$$ ACB = $$\angle$$ AED (corresponding angles)

Thus, $$\angle$$ ABC $$\sim$$ $$\angle$$ ADE

$$\therefore$$ $$\frac{AB}{AD}=\frac{AC}{AE}$$

Using componendo and dividendo, we have = $$\frac{AD}{DB}=\frac{AE}{EC}$$

=> Ans - (D)

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