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Consider the incomplete paragraph proof.
Because triangle XYZ is a right triangle, the side lengths
Given: Isosceles right triangle XYZ (45°-45°-90°
must satisfy the Pythagorean theorem, a? + b2 c2
triangle)
which in this isosceles triangle becomes a2 + a? = c?. By
Prove: In a 45°-45°-90° triangle, the hypotenuse is V2
combining like terms, 2a? c2.
times the length of each leg.
Which final step will prove that the length of the
hypotenuse, c, is /2 times the length of each leg?
• Substitute values for and c into the original
Pythagorean theorem equation.
O Divide both sides of the equation by two, then
determine the principal square root of both sides of the
equation.
Determine the principal square root of both sides of
the equation.
O Divide both sides of the equation by 2.

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

https://brainly.com/question/343682

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