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State and prove the Pythagoras theorem and select, this theorem is related to which triangle,

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Right angle triangle

Acute angle triangle triangle

Obtuse angle triangle triangle

None

answer is A.

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Detailed Solution

According to Pythagoras theorem, the square of hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides of the triangle.
Question Image

Let ABC is a triangle in which

∠ ABC = 90^{\circ}

Make,
BD ⊥ AC.
So, in △ADB and △ABC,

∠ A = ∠ A

[Common angle]

∠ ADB = ∠ ABC [Each {equal to 90}^{\circ}]

Thus, by the angle-angle criteria of congruency,

△ ADB \sim △ ABC

So, by ratio-side similarity rule,

\frac{AD}{AB} = \frac{AB}{AC}

Now,

{AB}^{2} = AD \times AC \dots . (1)

In the same way,

{BC}^{2} = CD \times AC \dots \dots . . (2)

On adding (1) and (2)

{AB}^{2} + {BC}^{2} = AD \times AC + CD \times AC

= AC (AD + CD)

= AC \times AC

Thus,

A B^{2} + B C^{2} = A C^{2}

So, we have proved the Pythagoras theorem.
The right-angle triangle is relevant to this theorem.
Option 1 is correct.

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