Question

15.in the given figure,AD perpendicular BC and BD<CD.
show that AB<AC​

Answer 1

Given :-

AD ⊥ BC, BD < CD.

To Prove :-

AB < AC

Proof :-

BD < CD

Squaring both sides.

⇒ BD² < CD²

Adding AD² on both sides.

⇒ BD² + AD² < CD² + AD² [In rt ∆ABD, BD²+

AD² = AB² & in

∆ACD, CD²+AD²

= AC²]

⇒ AB² < AC²

Square rooting both sides

⇒ AB < AC