Mathematics, 10.06.2020 06:57 SavannahP04

Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is StartRoot 2 EndRoottimes the length of each leg. Triangle X Y Z is shown. Angle X Y Z is 90 degrees and the other 2 angles are 45 degrees. The length of X Y is a, the length of Y Z is a, and the length of X Z is c. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2.

Which final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg?

Substitute values for a and c into the original Pythagorean theorem equation. 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.
Divide both sides of the equation by 2.

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Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle)...

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