Question

Triangle PQR is an isosceles right angled triangle at R.Prove that PQ square=2PR square

Answer 1

In ∆PQR,
PR=QR
ALSO ∆PQR IS Aright angle triangle so
PQ^2=PR^2+QR^2
PQ^2=2PR^2

Answer 2

PQ² = 2 PR²

Step-by-step explanation:

given data

angle PRQ = 90 degree

to find out

PQ² = 2 PR²

solution

As it is isosceles right angled triangle

so here $\angle$ P = $\angle$ Q .................1

so that

PR = QR    ...................2

so in triangle PQR , pythagorean theorem

PQ² = PR² + QR²    ...................3

put equation 2 value  in equation 3

PQ² = PR² + PR²

PQ² = 2 PR²

so hence proved

Learn more :

Abc is an isosceles triangle right angled at C.Prove that AB2=2AC2

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