In the given figure, O is a point inside a ∆PQR such that ∠PQR such that ∠POR = 90o, OP = 6cm and OR = 8cm. If PQ = 24cm and QR = 26cm, prove that ∆PQR is right-angled.
In the given figure, O is a point inside a ∆PQR such that ∠PQR such that ∠POR = 90o, OP = 6cm and OR = 8cm. If PQ = 24cm and QR = 26cm, prove that ∆PQR is right-angled.

 

 

 

Answer:

Applying Pythagoras theorem in right-angled triangle POR,

????????2 = ????????2 + ????????2

????????2 = 62 + 82

=>36 + 64

=>100

???????? = √100

=>10 ????????

In ∆ PQR,

????????2 + ????????2 = 242 + 102

=>576 + 100

=>676

????????2 = 262

=> 676

∴ ????????2 + ????????2 = ????????2

By applying Pythagoras theorem,

∆PQR is right-angled at P.