Can a triangle have three right Angles? If so, explain?

Question

it can exist, lots of examples all around us...

...get it....all "around" us..: ).. seems a few got it already. This was more than just a mathematical teaser as it is an exercise in trying to think outside what we're used to... In this case euclidean space and geometry, hope it was a little bit fun for all .. : )

Answer 1

As some of the above posters have pointed out, in Euclidean geometry ( standard highschool geometry ) a triangle has interior angles whose measures total 180 degrees. A right angle, by definition, measures 90 degrees. Three such angles would yield a total measure of 270 degrees, contradicting the above corrolary of the parallel postulate.

Thus to construct a triangle with three right angles we must throw out the parallel postulate and move into the realm of noneuclidean geometries. In some noneuclidean geometries, the measure of the interior angles of a triangle total less than 180 degrees ( hyperbolic geometry ), and in others they total more than 180 degrees ( spherical geometry ). By spherical geometry, I mean the geometry of the surface of a sphere, like the earth.

In spherical geometry, "lines" are the great circles and "line segments" are arcs of great circles on the sphere. Consider the surface of the earth as a sphere. Consider two great circles that intersect at the north pole at right angles. ( For example the prime meridian, and a 90 degree line of longitude. ) These will constitute two sides of our triangle, with the third side lying on the equator. This will give a triangle with three right angles.

Answer 2

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The sum of the three angles in any triangle is 180. In a right triangle, one of the angles is a right angle which is 90 degrees. Therefore the sum of the other two acute angles in the right triangle must equal 90 degrees. That is the only relationship I know of.

Answer 3

Drawn on a globe, the sum of angles in a triangle is greater than 180 degrees. This is Euclidean geometry.

Answer 4

No. If you have a three right angles, you will have a square that's missing one side. As you know, the sum of all the angles in a trigange must add up to 180 degrees. The sum of three right angles is (90 degrees *3 = 270 degrees). Thus a triangle cann't have three right angles since it does not meet the requirements listed above.

Answer 5

Of course it is possible.
You don't have to constrain yourself
to Euclidean geometry. Draw three straight
lines on a globe with vertices at the north pole,
and the other two on opposite sides of the equator.
This satisfies the definition of a triangle and has three
90 degree angles.

But you knew that, didn't you?
What is most interesting is the number of people who
bashed your intelligence without realizing they were wrong.

Answer 6

No.

A triangle is by definition a closed polygon. If even two right angles connected the three individual sides the figure would never be closed. Therefore a triangle must be less than 180 degrees and greater than 0 degrees.

Answer 7

a triangle can't even have 2 right sides. A triangle has 180 degrees when you add up all the angles together. So 2 right angles equal 180 degrees and an open sided figure. a triangle is a closed sided figure.

Answer 8

No because 3 right angles would equal 270 degrees whereas a triangle only has 180 degrees

Answer 9

it main property of a triangle is that it is a figure with three sides. the sum of the inner angles of a triangle is 180 degree. now 1 right angel measurs 90 n three would 270 so practicallt it is not possible.

Answer 10

No, because 3 right angles would equal 270 degrees whereas a triangle only has 180 degrees.