In a $Δ A B C$ , BD and CE are the altitudes. Prove that $Δ A D B$ and $Δ A E C$ are similar. Is $Δ C D B \sim Δ B E C$ ? [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

In $Δ A B D$ and $Δ A E C$ , we have

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

$∠ B A D = ∠ E A C$

So, by AA-criterion of similarity, we have

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

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

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