Question

in triangle ,if angle A=90 then prove that BC^2=AB^2+AC^2​

Answer 1

Answer:

ANSWER

Given: In △ABC,m∠B=90

o

To prove: AC

2

=AB

2

+BC

2

Construction: Draw BD⊥AC

Proof: We know that: If a perpendicular is drawn from the vertex of the right angle of a right angled triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

△ADB∼△ABC

So,

AB

AD

=

AC

AB

(Sides are proportional)

or AD.AC=AB

2

....(1)

Also, △BDC∼△ABC

So,

BC

CD

=

AC

BC

CD.AC=BC

2

...(2)

Or CD.AC=BC

2

....(2)

Adding (1) and (2)

AD.AC+CD.AC=AB

2

+BC

2

AC(AD+CD)=AB

2

+BC

2

AC.AC=AB

2

+BC

2

AC

2

=AB

2

+BC