Question
In the given figure, $\text{PA}\bot\text{AB},\text{QB}\bot\text{AB}$ and PA = QB. Prove that $\triangle\text{OAP}\cong\triangle\text{OBQ.}$ Is OA = OB?
✓
Answer
Given: In the figure,$\text{PA}\bot\text{AB},\text{QB}\bot\text{AB}$ and PA = QB.To prove: $\triangle\text{OAP}\cong\triangle\text{OBQ,}$
Is OA = OB?
Proof: In $\triangle\text{OAP}$ and $\triangle\text{OBQ,}$
$\angle\text{A}=\angle\text{B}$ (each 90°)
AP = BQ (given)
$\angle\text{AOP}=\angle\text{BOQ}$ (vertically opposite angles)
$\triangle\text{OAP}\cong\triangle\text{OBQ}$ (AAS condition)
OA = OB (c.p.c.t.)
Hence proved.
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