Question

Proof that it is a triangle​

Answer 1

Answer:

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

To prove: ∠B = 90°

Proof: We have a Δ ABC in which AC2 = AB2 + BC2

We need to prove that ∠B = 90°

In order to prove the above, we construct a triangle PQR which is right-angled at Q such that:

PQ = AB and QR = BC

From triangle PQR, we have

PR2 = PQ2+ QR2 (According to Pythagoras theorem,as ∠Q = 90°)

or, PR2 = AB2 + BC2 (By construction) …… (1)

We know that;

AC2 = AB2+BC (Which is given) …………(2)

So, AC = PR [From equation (1) and (2)]

Now, in Δ ABC and Δ PQR,

AB = PQ (By construction)

BC = QR (By construction)

AC = PR [Proved above]

So, Δ ABC ≅ Δ PQR (By SSS congruence)

Therefore, ∠B = ∠Q (CPCT)

But, ∠Q = 90° (By construction)

So, ∠B = 90°

Hence the theorem is proved.

Step-by-step explanation:

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