In a $△ A B C$ BD and CE are the altitudes. Prove that $△ A D B$ and $△ A E C$ are similar. Check whether $△ C D B a n d △ B E C$ are similar.

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Solution

In $△ A B D$ and $△ A E C$ , we have

$∠ A D B = ∠ A E C$ [Each equal to $90^{\circ}$ ]

$∠ B A D = ∠ E A C$ [Common]

So, by AA-criterion of similarity, we have

$△ B D A \sim △ C E A$ or, $△ A D B \sim △ A E C$ .

Clearly, $△ C D B$ is not similar to $△ B E C$ , because they are not equiangular.

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