True or False? In an obtuse triangle all the angles are obtuse. I think it's false but I'm not sure.
By definition of "obtuse", one of the angles must be greater than 90
So if all 3 angles would be obtuse, their sum would be greater than 270°
But we know that the total sum of all 3 angles = 180°
So, silly conclusion.
As a matter of fact , a triangle can have only one obtuse angle, if it had 2 we would already have a sum of more than 180°
Thank you!
True or False questions can often be answered by using logical reasoning or by recalling factual information. In this case, to determine if the statement is true or false, we need to understand the definitions of an obtuse triangle and an obtuse angle.
An obtuse triangle is a type of triangle in which one of the angles is an obtuse angle. An obtuse angle is any angle that measures more than 90 degrees, but less than 180 degrees.
Now, let's consider the statement: "In an obtuse triangle, all the angles are obtuse." We can apply logical reasoning to determine its correctness. Since an obtuse triangle has at least one obtuse angle, the statement implies that all angles in an obtuse triangle are obtuse. However, this is not true. An obtuse triangle can have one obtuse angle and two acute angles. Therefore, the statement is false.
To summarize, in an obtuse triangle, at least one angle is obtuse, but not all angles are obtuse.