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X.1 Acute, right, and obtuse triangles

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What are triangles?

Triangles are polygons with three sides and three angles. The size of the angles determines what kind of triangle it is.

Examples of triangles:
  • A triangle with all small angles
  • A triangle with one square corner
  • A triangle with one wide angle
Note

All the angles inside a triangle always add up to 180 degrees.

What is an acute triangle?

An acute triangle is a triangle where all three angles are less than 90 degrees.

How to identify:
  • Look for three sharp, narrow angles.
  • No angle looks like a square corner or a wide opening.
Example:
  • A triangle with angles measuring 40°, 70°, and 70° is acute.
Note

If every angle is less than 90°, the triangle is always acute.

What is a right triangle?

A right triangle has one angle that measures exactly 90 degrees. A 90-degree angle is shown with a small square in the corner.

How to identify:
  • Look for a square corner inside the triangle.
  • There is only one right angle in a triangle.
Example:
  • A triangle with angles measuring 90°, 40°, and 50° is a right triangle.
Note

Right triangles are often used in real life, such as in construction, ramps, and tools like squares.

What is an obtuse triangle?

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

How to identify:
  • Look for one wide, open angle that is bigger than a right angle.
  • The other two angles will always be smaller.
Example:
  • A triangle with angles measuring 120°, 30°, and 30° is obtuse.
Note

A triangle can only have one obtuse angle, because the angles must add up to 180°.

Comparing acute, right, and obtuse triangles

Each triangle type is named for the largest angle inside it.

Quick guide:
  • Acute triangle → all angles less than 90°
  • Right triangle → one angle exactly 90°
  • Obtuse triangle → one angle greater than 90°
Note

When classifying triangles, always check the angles first. The biggest angle decides the type of triangle.