Question

prove that conversation of Pythagoras Theorm

Answer 1

Solutions:-

In triangle

There are three sides

AB, BC and AC

Suppose that AB is perpendicular height

BC is base

And AC is Hypotenuse

Example :-

AB = 4 cm

BC = 3 cm

AC = ?

NOW,

BY Using Pythagoras theorem we can find AC

SO,

(AB)² + (BC)² = (AC)²

=> 4² + 3² = (AC)²

=> 16 + 9 = (AC)²

=> 25 = (AC)²

=> 5² = (AC)²

=> AC = 5 cm

Answer 2

Hello!! And Good Morning too!!!


Since the converse of Pythagoras Theorm says that "In a ∆,if square of one side is equal to the sum of the squares of the other two sides,then the angle opposite to the first side is a right angle.

So in pic(refer to attachment).

Given:In a triangle ABC,BC^2=AB^2+AC^2.

To prove : Angle A=90°.

Construction:Construct a ∆PQR such that angle P=90°,AB=PQ and AC=PR.

Proof:

In ∆PQR, angle P=90

By Pythagoras Theorem,we have
QR^2=PQ^2+PR^2
=> QR^2=AB^2 + AC^2

But BC^2=AB^2+AC^2
QR^2=BC^2 =>QR=BC.

IN ∆ABC and ∆PQR,

AB=PQ
AC=PR
BC=QR.

=>∆ABC is congruent to ∆PQR.(SSS)

=>Angle A=Angle P.

=>Angle A=90° (Since angle P=90°)

Q.E.D.


HOPE IT HELPS:)