In the given figure, sides AB and AC of △ABC have been produced to D and E respectively. If ∠CBD = x° and ∠BCE = y° such that x > y, show that AB > AC.

Given,

x > y

⇒ ∠CBD > ∠BCE

⇒ 180° - ∠CBD < 180° - ∠BCE

⇒ ∠ABC < ∠ACB

⇒ AC < AB (If two angles of a triangle are unequal, the greater angle has the greater side opposite to it)

⇒ AB > AC.

Hence, proved that AB > AC.