\triangle A D E ∼ \triangle A C B .

ICSE Class X Math 2015 Solved Paper - Question 47

$A B C$ is a right angled triangle with $∠ A B C=$ $90^{∘} . D$ is any point on $A B$ and $D E$ is perpendicular to AC. Prove that :

Question : 47 of 52

Marks: +1, -0

△ A D E ∼ △ A C B .

Solution:

To Prove :

△ {\ADE} ∼ △ {\ACB}

(i) In

△ {\ADE}

and

△ {\ACB}

\;\text " (1) "\; \;\; ∠ {\A}\;=∠ {\A} \;\; \;\text " [common] "\;

(2)

∠ {\AED}\;=∠ {\ABC}

\;=90^{∘} \;\text " (given) "\;

∴ △ {\ADE} ∼ △ {\ACB}

[AA axiom]

Go to Question:

Prev Question

Next Question