Question

in the given figure triangle ABC is right angled at B .... such that angle BCA=2 angle BAC... show that hypotenuse AC= 2 BC...​

Answer 1

ANSWER

In △ABD and △ABC we have BD=BC

AB=AB [Common]

∠ABD=∠ABC=90°

∴ By SAS criterion of congruence we get

△ABD≅△ABC

⇒AD=AC and ∠DAB=∠CAB [By CPCT]

⇒AD=AC and ∠DAB=x [∴∠CAB=x]

Now, ∠DAC=∠DAB+∠CAB=x+x=2x

∴∠DAC=∠ACD

⇒DC=AD [Side Opposite to equal angles]

⇒2BC=AD since DC=2BC

⇒2BC=AC Since AD=AC

Hence proved.

Answer 2

Answer:

=] DC = AD

=> 2BC = AD since DC = 2BC

=> 2BC = Ac Since AD = Ac

Hope it will be helpful ✌️