28. The Obtuse Triangle · When one angle steals the show

Try to break it

Drag the corners A, B, and C. Watch angle B closely. Can you make it smaller than 90°? What happens to the triangle's name when it changes?

How you build it

Make an obtuse triangle.

• Place point A — the first vertex of the triangle.
• Place point B at a moderate distance from A.
• Place point C so the triangle has one angle greater than 90° — that makes it obtuse.
• Draw side AB.
• Draw side AC.
• Draw side BC. One angle > 90° — that's the obtuse angle.

The proof, step by step

Prove that the triangle is obtuse-angled — one angle is greater than 90°.

• Identify the angle that is greater than 90°.
• Verify that this angle is indeed obtuse.
• Conclude that the triangle is obtuse-angled.

Worked example

In the given figure, triangle ABC has angle B = 100°. What type of triangle is ABC?

Since angle B is 100°, which is greater than 90°, triangle ABC is an obtuse-angled triangle.

• Acute-angled triangle
• Right-angled triangle
• Obtuse-angled triangle — correct
• Equilateral triangle