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Question -

ABCD is a quadrilateral in which AD = BC and тИа DAB = тИа CBA (see figure). Prove that

(i) тИЖABD тЙЕ тИЖBAC
(ii) BD = AC
(iii) тИаABD = тИа BAC



Answer -

In quadrilateral ACBD, we have AD = BC and тИа DAB = тИа CBA

(i) In тИЖ ABC and тИЖ BAC,
AD = BC (Given)
тИаDAB = тИаCBA (Given)
AB = AB (Common)
тИ┤ тИЖ ABD тЙЕ тИЖBAC (By SAS congruence)

(ii) Since тИЖABD тЙЕ тИЖBAC
тЗТ BD =AC [By C.P.C.T.]

(iii) Since тИЖABD тЙЕ тИЖBAC
тЗТ тИаABD = тИаBAC [By C.P.C.T.]

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