Question

ΔABC is an isosceles right angled triangle having ∠C = 90°. If D is any point on AB, then (AD)square+ (BD)square is equal to

Answer 1

Given:

ΔABC is an isosceles right angled triangle having ∠C = 90°

To Find:

AD² + BD²

Solution:

1) As we all know that the ABC is an isosceles triangle with an angle 90° so it is very clear that this triangle is the right angle.

2) So we will apply the Pythagoras theorem is the triangle ABC

we get,

AB²  = BC² + AC²

3) We all know this very well that D is the point on the  side AB so AB must be equivalent to the BD + DA.

we get,

(BD + DA)² = BC² + AC²

4) Now we will apply the formula of the  (a+b)²  = a² + b² + 2ab

we get,

BD² + AD² + 2 BD×AD = BC² + AC²

BD² + AD² = BC² + AC² - 2 BD×AD.