Prove that \triangle A B C ∼ \triangle D E C

ICSE Class X Math 2013 Solved Paper - Question 13

In the given figure, $A B$ and $D E$ are perpendicular to $B C$ .

Question : 13 of 46

Marks: +1, -0

Prove that

△ A B C ∼ △ D E C

Solution:

From

△ {\ABC}

and

△ {\DEC}

∠ {\ABC}\;=\;∠ {\DEC}

\;=90^{∘} \;\; \;\text " (Given) "\;

\;\text " and "\; \;\; ∠ {\ACB}=\;∠ {\DCE} \;\text " (Common) "\;

∴ \;\; △ {\ABC}\;∼\;∆ {\DEC}

\;(\;\text " By AA similarity) "\;

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