Question

ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig. 7.17). Prove that

(i) ΔABD ΔBAC

(ii) BD = AC

(iii) ABD = BAC.

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Answer 1

Answer:

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Attached

Answer 2

Answer:

As per given in the question,

∠DAB = ∠CBA and AD = BC.

(i) ΔABD and ΔBAC are similar by SAS congruency as

AB = BA (common arm)

∠DAB = ∠CBA and AD = BC (given)

So, triangles ABD and BAC are similar

i.e. ΔABD ≅ ΔBAC. (Hence proved).

(ii) As it is already proved,

ΔABD ≅ ΔBAC

So,

BD = AC (by CPCT)

(iii) Since ΔABD ≅ ΔBAC

So, the angles,

∠ABD = ∠BAC (by CPCT).