Are all isosceles triangles acute?

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Answer 1 · 2018-05-27T12:57:24

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

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 $180°$