8. ABCD is a rectangle in which diagonal AC bisects LA as well as LC. Show that: (&) ABCD is a square (il. diagonal BD bisects LB as well as LD.

(i) Consider triangles ADC and ABC, L DAC = L BAC [AC is bisector of LA] L DCA = L BCA [AC is bisector of LC] AC is common. .. 4ADC MBC AD = AB. [ASA] [CPCTJ As in rectangle ABCD, adjacent sides are equal. Hence ABCD is a square. (ii) Consider triangles DAB and BCD, AB = BC = CD = DA [Sides of a square] BD is common. 4 DAB 4 DCB L ADB = L CDB [SSS! [CPCTJ 114 and L ABD = L CBD :. BD bisects LB and LD. [CPCT) [Using above results]