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Classify triangles by angles

Triangles are classified by the measures of their interior angles: an acute triangle has three angles less than 90°, a right triangle has one angle exactly 90°, and an obtuse triangle has one angle greater than 90°. Classification depends on angle measures rather than orientation or side lengths; trigonometric calculations and formal geometric proofs are not included.

Detailed Explanation: Classify triangles by angles

To classify a triangle by its angles, look at the measure of each interior angle.

  • Acute triangle: All three angles are less than 90∘90^\circ.
  • Right triangle: One angle is exactly 90∘90^\circ.
  • Obtuse triangle: One angle is greater than 90∘90^\circ.

The triangle’s position, shape direction, or side lengths do not matter. Focus only on the angle measures.

Example: A triangle has angles measuring 45∘45^\circ, 90∘90^\circ, and 45∘45^\circ.

  1. Look at the angle measures: 45∘45^\circ, 90∘90^\circ, and 45∘45^\circ.
  2. One angle is exactly 90∘90^\circ.
  3. Therefore, the triangle is a right triangle.
The triangle is a right triangle.\boxed{\text{The triangle is a right triangle.}}

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