ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that (i) Δ ABD ≅ Δ BAC (ii) BD = AC (iii) ∠ ABD = ∠ BAC.

Question

ABCD is a quadrilateral in which AD = BC and &#x2220; DAB = &#x2220; CBA (see Fig. 7.17). Prove that (i) &#x394; ABD &#x2245; &#x394; BAC (ii) BD = AC (iii) &#x2220; ABD = &#x2220; BAC.

Philoid · Accepted Answer

It is given in the question that:

AD = BC and

∠DAB = ∠CBA

(i) In

AB = BA (Common)

∠DAB = ∠CBA (Given)

AD = BC (Given)

Therefore,

By SAS congruence,

(ii) Since,

Therefore,

BD = AC (By c.p.c.t)

(iii) Since,

Therefore,

∠ABD = ∠BAC (By c.p.c.t)

ABCD is a quadrilateral in which AD = BC and∠ DAB = ∠ CBA (see Fig. 7.17). Prove that(i) Δ ABD ≅Δ BAC(ii) BD = AC(iii) ∠ ABD = ∠ BAC.

ABCD is a quadrilateral in which AD = BC and∠ DAB = ∠ CBA (see Fig. 7.17). Prove that
(i) Δ ABD ≅Δ BAC

(ii) BD = AC

(iii) ∠ ABD = ∠ BAC.