Question

In triangle ABC, AB = AC and BD is perpendicular to AC. Prove that: 2 − 2 = 2 ×

Answer 1

Answer:

ABC is a isosceles triangle in which AB=AC

BD Perpendicular to AC

In △ABD

AB

2

=AD

2

+BD

2

...(Pythagoras theoram)

∴AC

2

=AD

2

+BD

2

....(as AB=AC) ...(1)

From diagram, we see that

⇒AC=CD+AD

⇒AC

2

=(CD+AD)

2

From (1) we get,

⇒(CD+AD)

2

=AD

2

+BD

2

CD

2

+AD

2

+2(CD×AD)=AD

2

+BD

2

CD

2

+2(CD×AD)=BD

2

...(AD square gets cancelled from both sides)

BD

2

−CD

2

=2(CD×AD)

Hence proved.