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The hypotenuse is times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes and this can be evaluated by using properties of isosceles triangle.
According to the statement
we have given that a theorem and we have to prove it.
So, For this purpose,
The given information is :
Isosceles triangle XYZ where
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.
Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now use Pythagoras theorem
But here a= b then the equation become
Then after solving it become
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
From this it is clear that the
it can be concluded that the hypotenuse is times the length of each leg 'a'.
Learn more about Pythagoras theorem here
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