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No. Here's why: you have a² + b² = c². If a is odd, then a² will also be odd (and if a is even, then a² will also be even. Same goes true for b² and c².
If a² & b² are both odd, then you have odd + odd, which is even. Why is {odd + odd} always even, you may ask. An informal proof could be something like this:
- Let m & n be non-zero integers.
- So 2m and 2n are guaranteed to be even,
- then (2m + 1) & (2n + 1) are both odd.
- Add them together: (2m + 1) + (2n + 1) = 2m + 2n + 2 = 2(m + n + 1) which is even.
And why is a² odd, when a is odd: if a is odd, then it does not have 2 as one of its factors. Since you square the number, you have not added any additional factors, so it still does not have 2 as a factor. If a was even, then it will have 2 as a factor, when you square it, you now have 2 as well as 2² as a factor, so the square is even as well.
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How do you find the hypotenuse to a triangle?
First of all, you have to make sure that it's a RIGHT triangle. That means that one of the angles in the triangle is 90 degrees. If not, then it's not a right triangle, and it doesn't have a hypotenuse. If it IS a right triangle, then the longest side is the hypotenuse.
Do A triangle with sides of lengths 32 60 and 68 is a right triangle?
Yes, the triangle is right-angled because 322 + 602 = 682. Given all three side lengths, you can use the Pythagorean relationship to determine whether a triangle is or is not right-angled. The right angle would be opposite the hypotenuse, 68.
Name all types of triangles for which the point of concurrency is inside the triangle?
The answer depends on what point of concurrency you are referring to. There are four segments you could be talking about in triangles. They intersect in different places in different triangles. Medians--segments from a vertex to the midpoint of the opposite side. In acute, right and obtuse triangles, the point of concurrency of the medians (centroid) is inside the triangle. Altitudes--perpendicular segments from a vertex to a line containing the opposite side. In an acute triangle, the point of concurrency of the altitudes (orthocenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Perpendicular bisectors of sides--segments perpendicular to each side of the triangle that bisect each side. In an acute triangle, the point of concurrency of the perpendicular bisectors (circumcenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Angle bisectors--segments from a vertex to the opposite side that bisect the angles at the vertices. In acute, right and obtuse triangles, the point of concurrency of the angle bisectors (incenter) is inside the triangle.
Do all of the angles on a right angled triangle have to be the same?
No a right angled triangle consists of two acute angles and one right angle
Is a scalene triangle is a right triangle?
A scalene triangle is one where all the angles are different and all the lengths of the sides are different. A standard 3, 4, 5 triangle does fit the definition of a scalene triangle, but we would alway refer to it in the more specific case, in this case a right angled triangle.
