Question

in an isosceles triangle PQR , PQ = QR and PR2 = 2 PQ2 . prove that angle Q is a right angle

Answer 1

PR^2 = 2 PQ^2

PR^2 = PQ^2 + QR^2

Therefore, by the converse of Pythagoras theorem,

Q is 90 degrees.

Answer 2

Answer:

The ∠Q is a right angle is proved.

Step-by-step explanation:

A right triangle:-

• A triangle in which one angle equals exactly 90°.
• A right triangle satisfies the Pythagoras theorem.
• The Pythagoras theorem states - "The square of the hypotenuse is equal to the sum of squares of the other two sides."

Step 1 of 1

Given:-

ΔPQR is an isosceles triangle such that PQ = QR and $PR^2=2PQ^2$.

To prove:-

The ∠Q is a right angle.

We need to show that the ∠Q = 90°.

It is given that ΔPQR is an isosceles triangle such that PQ = QR.

Also,

$PR^2=2PQ^2$

$PR^2=PQ^2+PQ^2$

Since PQ = QR. So,

$PR^2=PQ^2+QR^2$

This implies the ΔPQR satisfies the Pythagoras theorem.

As PR = The hypotenuse of the triangle

And PQ and QR are the two perpendicular sides of the triangle.

Therefore, ∠Q = 90°.

Hence the ∠Q is a right angle is proved.

#SPJ3