[[1]] in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of two sides.

# [[1]] in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of two sides.

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### Solution:

A right-angled triangle ABC which is right-angled at B
To prove:
Construction: Draw a perpendicular BD from B to AC

Proof:-
In triangle ABC and ABD

AA similarity criterion :- It states that if two triangles have two pairs of congruent angles, then the triangles are similar.
Now, Applying properties of similar triangles, we have corresponding sides proportional to each other.

Similarly,
Again, Applying properties of similar triangle, we have corresponding sides proportional to each other

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

Taking AC common, we get

And from the figure we know that AD + CD = AC
After changing the obtained value of AC above in equation (3), we get

in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of two sides.

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