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 $90^\circ )$
$AP = BQ ($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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