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Q: Why can't the Pythagorean theorem be used without a right angle?

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With right angle triangles

Simply because the Pythagorean Theorem is not true for any triangle that doesn't have a right angle in it. If a triangle has a right angle in it, then it satisfies the Theorem. If it hasn't, then it doesn't. And if it satisfies the Theorem, then it has a right angle in it, and if it doesn't, then it hasn't.

With any right angle triangle

A right angle triangle.

The Pythagorean Theorem states that in a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. The converse of the Pythagorean theorem states that, if in a triangle with sides a, b, c, a2 + b2 = c2 then the triangle is right and the angle opposite side c is a right angle.

When working out the sides of a right angle triangle.

Right-Angle triangles

Right angle triangles

No. The Pythagorean theorem applies only to right triangles...those containing a right angle (90 degrees).

All right angle triangles

All right angle triangles

A right angle is an angle of 90 degrees. Any angle not 90 degrees is not a right angle. End of story.

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