Question

plz solve this therom​

Answer 1

Proof: Construct another triangle, △EGF, such as AC = EG = b and BC = FG = a.

Converse of Pythagorean Theorem Proof

In △EGF, by Pythagoras Theorem:

EF2 = EG2 + FG2 = b2 + a2 …………(1)

In △ABC, by Pythagoras Theorem:

AB2 = AC2 + BC2 = b2 + a2 …………(2)

From equation (1) and (2), we have;

EF2 = AB2

EF = AB

⇒ △ ACB ≅ △EGF (By SSS postulate)

⇒ ∠G is right angle

Thus, △EGF is a right triangle.

Hence, we can say that the converse of Pythagorean theorem also holds.

Hence Proved.

Answer 2

Answer:

Statement:-In a triangle, if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the first side is a right angle.

Given:-

In Triangle ABC,

AC² = AB² + BC²

Construction: -

Construct a triangle PQR such that AB = PQ and BC = QR and Angle Q = 90°

Proof: -

In Triangle PQR,

Angle Q = 90°  (By construction)

PR² = PQ² + QR² (By Pythagoras Theorem)

PR² = AB² + BC² (Using PQ = AB and QR = BC by Construction)----Equation 1

Also,

AC² = AB² + BC² (Given)--------- Equation 2

Equating Equation 1 and Equation 2,

PR² = AC²

PR = AC

Now, In Triangle ABC and Triangle PQR,

AB = PQ (By Construction)

BC = QR (By Construction)

AC = PR (Proved Above)

Triangle ABC is congruent to triangle PQR by SSS

Angle B = Angle Q = 90°

This shows that Triangle ABC is right angled.

Hence Proved

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