Are all isosceles triangles acute?

May 27, 2018

No. There can be an obtuse angle or a right-angle in an isosceles triangle.

Explanation:

No. You can three types of isosceles triangles:

acute-angled isosceles triangle
All the angles are acute and the base angles are equal.

eg: 75°, 75°, 30°" or "50°, 50°, 80°

right-angled isosceles triangle
One angle is 90° and the other two are both 45°

45°, 45°, 90°" "larr" " (like one of the usual set squares)

obtuse-angles isosceles triangle
One angle is obtuse and the base angles are equal.

eg: 30°, 30°, 120°" or "25°, 25°, 130°

Of course there can only be one 90° or  one obtuse angle in a triangle. The other two angles MUST be acute, else the sum would be more than 180°