How to use diagram of the triangle.
To prove the Pythagorean theorem and use the triangle.
Important Triangles Solutions for Class 10th Maths, EXERCISE 6.6, Questions No:4
NCERT Books for Session 2022-2023 are based on CBSE Board.
ABC is a triangle in which ∠ ABC < 90° and AD ⊥ BC. Prove that AC² = AB² + BC² –2 BC . BD.
Share
In ΔADB, by pythagoras theorem
AD² + DB² = AB²
⇒ AD2 = AB2 – DB2 …(1)
In ΔADC, by pythagoras theorem, AD² + DC² = AC²
⇒ AB² – BD² + DC² = AC² [From the equation (1)]
⇒ AB² – BD² + (BC – BD)² = AC²
⇒ AC² = AB² – BD² + BC² + BD² – 2BC × BD = AB² + BC² – 2BC × BD