Question

State and Prove Baudhayan Theorem.

Diagram is not necessary. Proof and others are important.

Be brainly

Answer 1

Baudhayan Theorem is nothing but Phythagoras Theorem.


Statement: In a right angled triangle, the square of hypotenuse is equal to the sum of squares of other two sides.

Given:
In a right angled triangle ABC, Angle A = 90°

To prove:
BC×BC = (AB×AB) + (AC×AC)

Construction:
Draw AD perpendicular to BC.

Answer 2

Answer:

Baudhayana theorem states that

"The areas produced separately by the length and the breadth of a rectangle together equal the areas produced by the diagonal".

The diagonal and sides referred to are those of a rectangle, and the areas are those of the squares having these line segments as their sides. Since the diagonal of a rectangle is the hypotenuse of the right triangle formed by two adjacent sides, the statement is seen to be equivalent to the Pythagoras theorem.

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

Proof:

Given, a triangle ABC in which ∠ABC is 90°.

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

In ΔABD and ΔABC we have,

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

∠ABC = ∠ADB = 90°

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

So AD/AB= AB/AC

AB2 = AD×AC ...(1)

In ΔBDC and ΔABC we have,

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

∠ABC = ∠ADC = 90°

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

So DC/BC=BC/AC

BC2 = AC×DC ...(2)

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

⇒AB2 + BC2 = AD×AC + AC× DC⇒AB2 + BC2 = AC(AD + DC)⇒AB2 + BC2 = AC(AC)⇒AB2 + BC2 = AC2

AB2 + BC2 = AD×AC + AC× DC⇒AB2 + BC2 = AC(AD + DC)⇒AB2 + BC2 = AC(AC)⇒AB2 + BC2 = AC2Hence, proved