Question

Prove that sum of the angles in a triangle is 90 degree.​

Answer 1

Answer:

The sum of interior angles of a triangle is 90 degree

Correct answer:

The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.

Answer 2

Answer:

To prove: ∠B = 90°

Step-by-step explanation:

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.

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°)

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.

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