g. In the figure (12.25), QX and RX are the bisectors of the anglesQ and R respectively of the triangles PQR. If XS LQR andXT L PQ. Prove that8T.(ü) PX bisects the angle P

g. In the figure (12.25), QX and RX are the bisectors of the anglesQ a

1.	g. In the figure (12.25), QX and RX are the bisectors of the anglesQ and R respectively of the triangles PQR. If XS LQR andXT L PQ. Prove that8T.(ü) PX bisects the angle P
Answer» Solution:Angle XSQ = 90°Angle XTQ = 90°QX = QX (This is the common side)Since QX bisects Q the angle is equally split between the triangles)So, XQS = TQXSo,Δ XTQ is congruent toΔ XSQXS = XT (According toCPCT) ...(1)Draw XW perpendicular to PRSimilarly, we can prove thatΔ XSR is congruent toΔ XWR.So, XS = XW ... (2)So, from (1) and (2)now in PXT and PXW, PTX = PWX, PX is common and XT = XW.BY R.H.S. both triangles are congruent, XPT = XPW and PX bisects the angle P. Hence proved