Understanding Obtuse Triangles: Characteristics and Classification

Regarding side length, a triangle is an obtuse triangle if …

A triangle is classified as an obtuse triangle based on the measurement of its angles

A triangle is classified as an obtuse triangle based on the measurement of its angles. An obtuse triangle is defined as a triangle that has one angle greater than 90 degrees.

To determine if a triangle is obtuse, we need to compare the measures of its angles. The sum of all angles in a triangle is always 180 degrees.

Let’s consider the three angles of a triangle: angle A, angle B, and angle C.

If one of the angles (let’s say angle A) is greater than 90 degrees, then the triangle is automatically classified as an obtuse triangle. This is because the other two angles (angles B and C) must be acute angles (less than 90 degrees) since the sum of all three angles is 180 degrees.

However, if angle A is less than or equal to 90 degrees, we cannot determine if the triangle is obtuse based on that information alone. In such cases, we need to consider the other angles (B and C).

If both angle B and angle C are acute (less than 90 degrees), then the triangle is classified as an acute triangle. This is because the sum of all three acute angles will be less than 180 degrees.

On the other hand, if at least one of the angles (angle B or angle C) is greater than 90 degrees, then the triangle is classified as an obtuse triangle. In this scenario, the sum of the two acute angles and the obtuse angle will be greater than 180 degrees.

Therefore, a triangle is classified as an obtuse triangle if it has one angle greater than 90 degrees and the remaining acute angles are less than 90 degrees.

To summarize:
– If one angle is greater than 90 degrees, the triangle is obtuse.
– If all three angles are less than 90 degrees, the triangle is acute.
– If two angles are less than 90 degrees and one angle is greater than 90 degrees, the triangle is obtuse.

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