Classify triangles by angle type

Triangles are classified by the measures of their interior angles: acute triangles have three angles less than $90^\circ$ , right triangles have exactly one $90^\circ$ angle, and obtuse triangles have exactly one angle greater than $90^\circ$ . This classification relies on the $180^\circ$ angle sum, so a triangle cannot have two right or obtuse angles, and supports later reasoning about geometric properties and measurement.

Detailed Explanation: Classify triangles by angle type

To classify a triangle by its angle type, look at the measures of its three interior angles:

Acute triangle: all three angles are less than $90^\circ$ .
Right triangle: exactly one angle is $90^\circ$ .
Obtuse triangle: exactly one angle is greater than $90^\circ$ .

The angles in every triangle add to $180^\circ$ .

Example: Classify a triangle with angles $55^\circ$ , $90^\circ$ , and $35^\circ$ .

Check the angle measures:
- $55^\circ$ is less than $90^\circ$ .
- $90^\circ$ is exactly $90^\circ$ .
- $35^\circ$ is less than $90^\circ$ .
The triangle has exactly one $90^\circ$ angle.
Therefore, the triangle is a right triangle.

Check:

55^\circ+90^\circ+35^\circ=180^\circ

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Triangle Classification - Angles

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Classify triangles by angle type

Detailed Explanation: Classify triangles by angle type

Learn by doing: Classify triangles by angle type

Practice with unlimited practice problems

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Triangle Classification - Angles