Question

if in a anglePQR,PR2=PQ2 +QR2 ,then the right angle of PQR is at the vertex​

Answer 1

Answer:

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Class 7

>>Maths

>>The Triangle and Its Properties

>>Right Angled Triangles and Pythagoras Property

>>In Δ PQR , if PR^2 = PQ^2 + QR^2 , prove

Question

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In ΔPQR, if PR

2

=PQ

2

+QR

2

, prove that ∠Q is right angle.

Medium

Solution

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This is converse of Pythagoras theorem

We can prove this contradiction sum q

2

=p

2

+r

2

in ΔPQR while triangle is not a rightangle

Now consider another triangle ΔABC we construct ΔABC AB=qCB=b and C is a Right angle

By the Pythagorean theorem (AC)

2

=p

2

+r

2

But we know p

2

+r

2

=q

2

and q=PR

So (AB)

2

=p

2

+r

2

=(SR)

2

Since PQ and AB are length of sides we can take positive square roots

AC=PQ

All the these sides ΔABC are congruent to ΔPQR

So they are congruent by sss theorem

solution