In a $△ A B C$ , BD and CE are the altitudes. Prove that $△ A D B a n d △ A E C$ are similar. Is $△ C D B \sim △ B E C$ ?

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Solution

In $△ A B D a n d △ A E C$ , we have
$∠ A D B = ∠ A E C [E a c h$ equal to $90^{\circ}$ ]
$∠ B A D = ∠ E A C$

So, by AA-criterion of similarity, we have
$△ B D A \sim △ C E A o r, △ A D B \sim △ A E C$ .
Clearly, $△$ CDB is not similar to $△$ BEC, because they are not equiangular.

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