Question

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sᴛᴀᴛᴇ ᴀɴᴅ ᴘʀᴏᴠᴇ Pʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ. ​

Answer 1

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

Answer 2

Answer:

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• Pythagoras theorem is basically used to find the length of an unknown side and angle of a triangle. By this theorem, we can derive base, perpendicular and hypotenuse formula.

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• Given: A right-angled triangle ABC, right-angled at B.

• To Prove- AC² = AB² + BC²

• Construction: Draw a perpendicular BD meeting AC at D.

Proof:

We know, △ADB ~ △ABC

Therefore, AD/AB = AB/BC

(Corresponding sides of similar triangle)

or, BC² = CD × AC

Adding the equation (1) & (2) we get-

➪ AB² + BC² = AD × AC + CD × AC

➪ AB² + BC² = AC (AD+CD)

Since,

AD + CD = AC

Therefore,

AC² = AB² + BC²

Hence,The pythagorean Theorem is proved.

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