Question

the perpendicular op and oq drawn from the point o to ab and ac respectively, if are congruent. prove that ai is the bisector of cab
​

Answer 1

Answer:

Let us take Right triangle APO, right-angled at P,

OP is perpendicular to AB or APO = 90 °

Now,  

In triangle ΔAQO, right-angled at Q,

QO is perpendicular to AC or AQO = 90 °

Taking both triangles ΔAPO and ΔAQO,

AO = AO (Common Side)

APO = AQO = 90 °

AQ = AP (Perpendicular being drawn from same point O)

Hence, by SAS (Side-Angle-Side Congruence Condition)

ΔAPO ≅ ΔAQO,

So, QAO = BAO (Corresponding Parts of Congruent triangles )

Or we can conclude that AO is the bisector of \angle QAP,

marke me a brainilest