Question

Consider the incomplete paragraph proof.

Answer 1

The hypotenuse is $c = a\sqrt{2}$  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 $Angle X = 45^{0}$ $Angle Y = 45^{0}$ $Angle Z = 90^{0}$

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

$a^{2} + b^{2} = c^{2}$

But here a= b then the equation become

$a^{2} + a^{2} = c^{2}$

Then after solving it become

$2a^{2} = c^{2}$

And here we have to find the value of the hypotenuse,

so we solve it for c.

Then

$c = a\sqrt{2}$

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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