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11/07/2021 11:39 am
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ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig.). Prove that
(i) ΔABD ΔBAC
(ii) BD = AC
(iii) ABD = BAC
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11/07/2021 11:40 am
The given parameters from the questions are DAB = CBA and AD = BC.
(i) ΔABD and ΔBAC are similar by SAS congruency as
AB = BA (It is the common arm)
DAB = CBA and AD = BC (These are given in the question)
So, triangles ABD and BAC are similar i.e. ΔABD ΔBAC. (Hence proved).
(ii) It is now known that ΔABD ΔBAC so,
BD = AC (by the rule of CPCT).
(iii) Since ΔABD ΔBAC
Angles ABD = BAC (by the rule of CPCT).