Step-by-step explanation:
Given data:
ABCD is a quadrilateral.
AD = BC – – – – (1)
∠DAB = ∠CBA – – – – (2)
To prove that BD = AC:
In ΔABD and ΔBAC,
AD = BC (given side)
∠DAB = ∠CBA (given angle)
AB = BA (reflexive side)
Therefore ΔABD ≅ ΔBAC by SAS congruence rule.
By corresponding parts of congruence triangles,
BD = AC
Hence proved.
