Question

state and prove phythagoras theoram
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Answer 1

In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity...

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Answer 2

$\huge\bf\underline\bold\blue{Explanation❄}$

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 the right-angled triangle are called base, perpendicular and hypotenuse .

According to Pythagoras theorem ,

$(AC) ^{2} =(AB) ^{2} + (BC) ^{2} (AC) ^{2} =(AB) ^{2} + (BC) ^{2}$

Proof:

Given, a triangle ABC in which ∠ABC is 900∠ABC is 900.

Construction: Draw a perpendicular BD on AC i.e. BD ⊥⊥ AC.

In ΔABD and ΔABC ΔABD and ΔABC we have,

∠BAD = ∠BAC ∠BAD = ∠BAC i.e. ∠A∠A is common in both triangles.

∠ABC = ∠ADB = 900∠ABC = ∠ADB = 900

Therefore ΔABC∼ΔABD ΔABC∼ΔABD ( By AA similarity i.e. angle-angle similarity)

So,⇒ADAB=ABAC

⇒AB2 = AD×AC ...(1)

In ΔBDC and ΔABC ΔBDC and ΔABC we have,

∠BCD = ∠BCA ∠BCD = ∠BCA i.e. ∠C∠C is common in both triangles.

∠ABC = ∠ADC = 900∠ABC = ∠ADC = 900

Therefore ΔABC∼ΔBDC ΔABC∼ΔBDC ( By AA similarity i.e. angle-angle similarity)

So,⇒DCBC=BCAC⇒BC2 = AC×DC ...(2)⇒DCBC=BCAC⇒BC2 = AC×DC ...(2)

Adding equation (1) and (2) , we get

⇒AB^2 + BC^2 = AD×AC + AC× DC

⇒AB^2 + BC^2 = AC(AD + DC)

⇒AB^2 + BC^2 = AC(AC)

⇒AB^2 + BC^2 = AC^2

Hence, proved.