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Sagot :
The hypotenuse is [tex]c = a\sqrt{2}[/tex] 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 [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]
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
[tex]a^{2} + b^{2} = c^{2}[/tex]
But here a= b then the equation become
[tex]a^{2} + a^{2} = c^{2}[/tex]
Then after solving it become
[tex]2a^{2} = c^{2}[/tex]
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
[tex]c = a\sqrt{2}[/tex]
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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