Question

Angles \(Q\) and \(R\) of a \(Δ\) \(PQR\) are \(25°\) and \(65°\). Write which of the following is true: 

1.  \(PQ^2 + QR^2= RP^2\) 
2.  \(PQ^2 + RP^2= QR^2\) 
3.  \(RP^2 + QR^2= PQ^2\)

Answer 1

The sum of the measures of all interior angles of a triangle is \(180\degree\).

\(\angle PQR + \angle PRQ + \angle QPR = 180\degree\)

\(25\degree + 65\degree + \angle QPR = 180\degree\)

\(90\degree + \angle QPR = 180\degree\)

\(\angle QPR = 180\degree - 90\degree = 90\degree\)

Therefore, \(Δ\) \(PQR\) is right-angled at point \(P\).

Hence, \((PR)^2 + (PQ)^2= (QR)^2\)

Thus, (ii) is true.