Q. ABC is an isosceles triangle right angled at C.
Prove that AB² = 2AC².
Given :
To Prove :
Proof :
Ιn ΔABC, ∠C = 90º
AB² = 2AC2
In ΔACB,
∠C =
900
AB2 =
AC2
+ BC2
... (i)
... [by Pythagoras theorem]
BC = AC
∴
... (ii)
BC2
= AC2
AB2 =
AC2 +
AC2
∴
... [From (i) and (ii)]
AB² =
∴
2AC2
ABC is an isosceles triangle right angled at C.
B
C
A
ΑC = BC
AB² =
2AC².
Ex.6.5 (Q.4)