An obtuse triangle has one angle whose measure is greater than 90^(∘).
Is it possible to draw an obtuse isosceles triangle? Yes Is it possible to draw an obtuse equilateral triangle? No Explanation: See solution.
Practice makes perfect
Let's consider the cases one at a time.
Obtuse Isosceles Triangle
An obtuse triangle is a triangle where the measure of one angle is greater than 90^(∘). Let's start with an arbitrary obtuse angle whose measure is 120^(∘).
Since we want the triangle to be isosceles, two of its sides must be congruent.
We have drawn an obtuse isosceles triangle. Note that there are infinitely many solutions for this exercise. We are just showing one of them.
Obtuse Equilateral Triangle
An equilateral triangle has three congruent sides. This makes all three angles congruent as well. Therefore, since the sum of the measures of the interior angles equals 180^(∘), we can find the measure of one interior angle.
180^(∘)/3=60^(∘)
The measure of each interior angle of an equilateral triangle is 60^(∘). Therefore, all the angles in an equilateral triangle are acute.
