Question

In given figure,
CF and AE are equal perpendiculars on BD, BF = FE = ED.
$\angle$BAE = ______.

• A. $\angle$BCD
• B. $\angle$CBA
• C. $\angle$ADC
• D. $\angle$DCF

Answer 1

Answer: (D)

$\angle$DCF

In $△ABE$ and $△CDF$

$\Rightarrow$ $AE=CF$ [given]

$\Rightarrow$ $\angle AEB=\angle CFD$ [given]

$\Rightarrow$ $BF+FE=DE+EF$

$\Rightarrow$ $BE=DF$

$\therefore$ $△ABE\cong △CDF$ [By SAS criteria]

$\therefore$ $\angle BAE=\angle DCF$ [By CPCT]