In Euclidean geometry, there can be _____ right angle(s) in a triangle.?

Answer 1

at most one

Answer 2

1

Answer 3

In Euclidean geometry, the sum of the interior angles of a triangle is 180 degrees.

Assume that there are two right angles in a triangle. Then, there are 180 degrees plus the measure of the third angle. So, the sum of the three interior angles of a triangle is greater than 180 degrees. This contradicts the Euclidean principle that the sum of the three interior angles is 180 degrees and shows that the assumption of two right angles in a triangle is false.

A contradiction also occurs if we assume a triangle has three right angles.

So, in Euclidean geometry, a triangle can have at most one right angle. That is, in Euclidean geometry, a triangle can have zero right angles or one right angle.

Answer: 0 or 1

Answer 4

0 or 1

Answer 5

You can only have, at most, 1 right angle in a triangle. A figure with only 2 right angles can be, at the minimum, an irregular pentagon. A triangle can have 0 right angles if it is acute (all angles measure less than 90 degrees), obtuse (all angles measure more than 90 degrees), or equiangular (all angles measure the same or exactly 60 degrees). 3 right angles will also produce an irregular pentagon. 4 right angles will make a quadrilateral. Anyway, a triangle can only have three angles (hint: "TRI"angle), so any figure with more than 3 angles cannot be a triangle, making it so that a triangle can only have 1 right angle.

Answer 6

1. The sum of angles is 180. If there was more than 1 (i.e. 2), then there would be no room left for the required number of angles (3).

Answer 7

Only one. If 3 segments form 2 right angles, then they can't form a triangle.

Answer 8

only 1

Answer 9

only 1

Answer 10

1.

Answer 11

190