Question

$AD,BE$ and $CF$, the altitude of $\Delta ABC$ are equal. Then

• A. $AC=BC$
• B. $AD=AB$
• C. $AB=CF$
• D. None of these

Answer 1

Answer: (A)

$AC=BC$

Given: $AD,BE$ and $CF$ are the altitude of $△ABC$ and are equal i.e $AD=BE=CF$

Claim $AC=BC$

Proof: Cosnider $△ADC$ and $△BEC$

$AD=BE$ (given)

$\angle ADC=\angle BEC$ (each ${90}^o$)

$\angle C=\angle C$ (common)

$△ADC\cong △BEC$ (By AAS)

$\therefore$ $AC=BC$ (By CPCT)

Hence proved