Solve this: Q Prove that ∆ABC is right-angled at A if AB = 2n + 1, AC = - Maths - Congruency of Triangles

Question

Solve this:

Q Prove that ∆ ABC is right-angled at A if
AB = 2n + 1, AC = 2n
(n+ 1) and BC = 2n (n + 1) + 1

Jegannathan Anandaraman · Answer

Hi Vinay Don dear, being A as 90 degree
Hypotenuse BC = 2n(n+1) + 1
Sides AB = 2n + 1
And AC = 2n (n+1)
For the triangle to be right angled we have to prove
BC^2 = AB^2 + AC^2
Plugging on R H S
(2n+1)^2 + [2n (n+1)]^2
==> [2n (n+1)]^2 + 4n^2 + 4n + 1
==> ​[2n (n+1)]^2 + 2* 2n (n + 1) + 1
==> A^2 + 2 * A * B + B^2 {here A = 2n(n+1), B = 1}
Thus we have (A+B)^2
That is [2n(n+1) + 1}^2 = L H S
Thus by converse of Pythagoras it is confirmed that BAC is a right
angled triangle

Solve this: Q. Prove that ∆ ABC is right-angled at A if AB = 2n + 1, AC = 2n (n+ 1) and BC = 2n (n + 1) + 1.

Solve this:

Q. Prove that $∆$ ABC is right-angled at A if AB = 2n + 1, AC = 2n (n+ 1) and BC = 2n (n + 1) + 1.