Question

D is a point on side BC of ΔABC, such that AD = AC
Show that AB > AD.

Answer 1

In ΔDAC,
AD = AC ..........(Given)
So, ∠ADC = ∠ ACD ........... (Angles opposite to equal sides)
Now, ∠ADC is an exterior angle for ΔABD.
So, ∠ADC > ∠ABD
or, ∠ACD > ∠ABD
or, ∠ACB > ∠ABC
So, AB > AC ...........(Side opposite to larger angle in ΔABC)
or, AB > AD ........(AD = AC)