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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.

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.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 6228 Points
3 months ago
(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]

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