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.