Question

D
ABCD is a quadrilateral in which AD = BC and
Z DAB = Z CBA (see Fig. 7.17). Prove that
(1) A ABD = ABAC
(ii) BD=AC
B
(I) ZABD = ZBAC.​

Answer 1

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✏ABCD is a quadrilateral

Given :-

↪AD = BC

↪/_DAB = /_CBA

To prove :-

$\huge\mathscr\pink{Answer :-1}$

1. ΔABD = ΔBAC

In ΔABD & ΔBAC

✏AD = BC [Given]

✏ /_DAB = /_CBA [Given]

✏AB = BA [Common]

✏ΔABD ≈ ΔBAC [ By SAS Rule]

$\huge\mathscr\pink{Answer:-2}$

Since:-

✏ΔABD ≈ ΔBAC

✏Then BD = AC [By CPCT ]

$\huge\mathscr\pink{Answer:-3}$

Since:-

✏ΔABD ≈ ΔBAC

✏Then /_ ABD = /_BAC [ By CPCT ]