Triangles
96. The Angle Identity · Acute, Right, or Obtuse — what's your triangle's name?
The sum of interior angles in any triangle is always 180°.
Triangles are classified by angles into three types: acute (all angles < 90°), right (one angle = 90°), and obtuse (one angle > 90°). Since the angles must sum to 180°, at most one can be ≥ 90°.
What this lesson covers
Try to break it
Try dragging C until one angle clicks exactly to 90°. See how it becomes a Right Angled Triangle? Now push C further out to widen an angle past 90° — it flips to Obtuse! Pull C straight up, and all three angles shrink below 90° — Acute!
How you build it
Place three points and join them edge by edge into a triangle.
- Place point A, the first vertex of the triangle.
- Place point B, the second vertex.
- Place point C, the third vertex.
- Draw the side from A to B.
- Draw the side from B to C.
- Draw the side from C to A to complete the triangle.
The proof, step by step
Prove that the type of a triangle is decided by its largest angle.
- The sum of interior angles in any triangle is always 180°.
- If one angle is 90°, the other two must share the remaining 90°, so both are acute.
- If one angle is >90°, the other two must share <90°, so both are acute. This is an obtuse triangle.
- If all three angles are <90°, the triangle is classified as acute angled.
Worked example
A triangle has angles measuring 45°, 60°, and 75°. How is this triangle classified based on its angles?
All three angles (45°, 60°, 75°) are less than 90°. By definition, a triangle where every angle is acute is classified as an acute angled triangle.
- Right Angled Triangle
- Obtuse Angled Triangle
- Acute Angled Triangle — correct
- Equilateral Triangle