Question

OD bisects $\angle AOB$. DA and DB are perpendiculars from D on the ray OA and OB. Show that DA $\cong$ DB.

Answer 1

ASA $\Rightarrow$ Angle sum Angle property

CPCT $\Rightarrow$ Congruent part of congruent triangle

Refer image,

first we will show

that $\Delta AOD\cong \Delta BOD$

So $\angle OAD=\angle OBD$ (${90}^0$)

$OD=OD$ (Common)

$\angle AOD=\angle BOD$ ($\because OD$ bisects $\angle AOB$ )

$\angle AOD\cong \angle BOD$ (by ASA property)

So, $DA\cong DB$ (by CPCT)

congruent part of congruent triangle