Question

➜ Proove the Pythagoras theorem!!!!✌️
​

Answer 1

Pythagoras/Pythagorean Theorem:

• In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
• States that in a right triangle that, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²).

In short it is written as: a² + b²= c²

Given: A ∆ XYZ in which ∠XYZ = 90°.

To prove: XZ² = XY² + YZ²

Construction: Draw YO ⊥ XZ

Proof: In ∆XOY and ∆XYZ, we have,

∠X = ∠X → common

∠XOY = ∠XYZ → each equal to 90°

Therefore, ∆ XOY ~ ∆ XYZ → by AA-similarity

⇒ XO/XY = XY/XZ

⇒ XO × XZ = XY² ----------------- (i)

In ∆YOZ and ∆XYZ, we have,

∠Z = ∠Z → common

∠YOZ = ∠XYZ → each equal to 90°

Therefore, ∆ YOZ ~ ∆ XYZ → by AA-similarity

⇒ OZ/YZ = YZ/XZ

⇒ OZ × XZ = YZ² ----------------- (ii)

From (i) and (ii) we get,

XO × XZ + OZ × XZ = (XY² + YZ²)

⇒ (XO + OZ) × XZ = (XY²+ YZ²)

⇒ XZ × XZ = (XY² + YZ²)

⇒ XZ² = (XY² + YZ²)

$itzDopeGirl$

Answer 2

Answer:

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°. The sides of a right triangle (say x, y and z) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

formula of pythagoras theorem is

${hypotenuse}^{2} = {base}^{2} + {perpendicular}^{2}$

or

${c}^{2} = {a}^{2} + {b}^{2}$

Where “a” is the perpendicular side,

“b” is the base,

“c” is the hypotenuse side.

The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.

Pythagoras Theorem Proof

Given: A right-angled triangle ABC.

To Prove- AC^2 = AB^2 + BC^2

Construction: Draw a perpendicular BD joining AC at D.

Proof: First, we have to drop a perpendicular BD onto the side AC

We know, △ADB ~ △ABC

Therefore, ADAB=ABAC (Condition for similarity)

Or, AB^2 = AD × AC……..(1)

Also, △BDC ~△ABC

Therefore, CDBC=BCAC (Condition for similarity)

Or, BC2= CD × AC........(2)

Adding the equations (1) and (2) we get,

AB2 + BC^2 = AD × AC + CD × AC

AB2 + BC^2 = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC^2 = AB^2 + BC^2

Hence, the Pythagorean theorem is proved.