In the given figure, AP = AQ and the right angles are shown. Which of the following statements can certainly be stated?
AB = AC
Since PB, AD and QC are perpendicular to the same line BC, they are parallel to each other i.e. PB || AD || QC.
Since, PB || AD || QC and PQ is a transversal making equal intercepts i.e. PA = AQ; therefore the other transversal BC will also make equal intercepts i.e. BD = CD.
Now in ΔABD and ΔACD.
(i) BD = CD [Proved above]
(ii) AD = AD [Common]
(iii) ∠ADB=∠ADC=90∘ [As, AD ⊥ BC]
∴ ΔABD=ΔACD [By SAS]
⇒ AB = AC [By C.P.C.T]