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10. In figure, OP perpendicular AB and OQ PerpendiAC. Prove that AO isbisector of ZCAB. ​

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,


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