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In figure below, if $AB\ ⊥\ BC$, $DC\ ⊥\ BC$, and $DE\ ⊥\ AC$, prove that $Δ\ CED\ ∼\ Δ\ ABC$.
"
Given:
In the given figure $AB\ ⊥\ BC$, $DC\ ⊥\ BC$, and $DE\ ⊥\ AC$.
To do:
We have to prove that $Δ\ CED\ ∼\ Δ\ ABC$.
Solution:
In $\vartriangle ABC$ and $\vartriangle CED$,
$\angle BAC+\angle BCA=90^o$
$\angle BCA+\angle ECD=90^o$
This implies,
$\angle BAC=\angle ECD$
In $\vartriangle ABC$ and $\vartriangle CED$,
$\angle ABC=\angle CED=90^o$
$\angle BAC=\angle ECD$
Therefore,
$Δ\ CED\ ∼\ Δ\ ABC$.
Hence proved.
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