Question

Prove that in a right angled triangle , the square of the hypotenuse is equal to the squares of remaining two sides

Answer 1

Here is your Answer......

Answer 2

figure is in the attachment

given

a right angled triangle ABC, right angled at B

to prove-AC square=BC square+AB square

CONSTRUCTION: draw perpendicular BD onto the side AC.

proof:

we know that if a perpendicular is drawn from the vertex of a right angle of a right angle triangle to the hypotenuse, then triangles on both side of the perpendicular are similar to the whole triangle and to each other.


We have

tangle ADB congruent triangle ABC. (by AA similarity)

Therefore, AD/AB=AB/AC


(In similar triangles corresponding sides are proportional)

AB square=AD*AC.........(1)


Also, triangle BDC congruent triangle ABC

Therefore,CD/BC=BC/AC

(In similar triangles corresponding sides are proportional)

Or, BC square=CD*AC ........(2)


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

AB SQUARE + BC SQUARE IS EQUAL TO 80 INTO A C + CD INTO AC

BC SQUARE + AC SQUARE IS EQUAL TO AC ( AD + CD)


(From the figure AD + CD is equal to AC)

A B SQUARE + BC SQUARE IS EQUAL TO AC. AC


Therefore, AC square is equal to AB square + BC SQUARE

THIS THEOREM IS KNOWN AS PYTHAGORAS THEOREM.....

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