Question

how to prove it this problem​

Answer 1

This is 7 class NCERT TEXTBOOK know
Chapter:triangles and it’s properties

Answer 2

Step-by-step explanation:

Given,DB = 3CD

Also,BC = CD + DB = CD + 3CD⇒ BC = 4CD [1]As, AD ⊥ BC,

By Pythagoras theorem i.e.(Hypotenuse)2 = (base)2 + (Perpendicular)2

In Δ ACD AC2 = AD2 + CD2 [2]

In ΔABD AB2 = AD2 + DB2

⇒ AB2 = AD2 + (3CD)2

⇒ AB2 = AD2 + 9CD2 [3]

Subtracting [2] from [3]

⇒ AB2 - AC2 = 9CD2 - CD2

⇒ AB2 = AC2 + 8CD2

⇒ 2AB2 = 2AC2 + 16CD2

⇒ 2AB2 = 2AC2 + (4CD)2

⇒ 2AB2 = 2AC2 + BC2

[From 1]Hence Proved.