Question

prove that converse of Pythagoras theorem.​

Answer 1

Answer:

Converse of the Pythagorean Theorem: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. Proof: ... By the Pythagorean Theorem, BD² = a² + b² = c², and so BD = c.

Answer 2

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Given :

• AC² = AB² + BC²

To prove :

• ABC is a right angled triangle.

Construction : Draw a right angled triangle PQR such that, angle Q = 90°, AB = PQ, BC = QR.

Proof :

In triangle PQR,

Angle Q = 90°

Also,

PR² = PQ² + QR² ( By using Pythagoras theorem )...(1)

AC² = AB² + BC² ( Given )

Also, AB = PQ and BC = QR

Therefore,

AC² = PQ²+ QR²....(2)

From eq (1) and (2),

PR² = AC²

So, PR = AC

Now,

In ∆ABC and ∆PQR,

AB = PQ

BC = QR

AC = PR

Hence,

∆ABC is congruent to ∆PQR by SSS criteria.

Therefore, Angle B = Angle Q ( By CPCT )

_____________________________

Angle Q = 90°

Therefore,

Angle B = 90°

Thus, ABC is a right angled triangle with Angle B = 90°

Hence proved.

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