Explanation
Concept:
The Pythagorean equation relates the sides of a right triangle in a simple way, so that if the lengths of any two sides are known the length of the third side can be found.
Calculations:
Given, in a triangle ABC, ∠A = 90° and D is mid-point of AC.
⇒ (AC)² = 2(AD)²....(1)
By Pythagorean theorem, we have
⇒ BC² = AB² + AC²
From equation (1), we have
⇒ BC² = AB² + 2(AD)²
And BD² = AB² + AD²
Consider, (BC)² - (BD)² = (AB)² + 2(AD)² - (AB² + AD²)
⇒ (BC)² - (BD)² = (AD)²
