Definition:

Properties:

• All angles of an acute triangle are acute angles (<90°).
• The sum of the angles in an acute triangle is always 180 degrees.
• Since all angles are less than 90 degrees, no side of the triangle can be a horizontal or vertical line.
• The longest side of an acute triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

Examples:

Here are some examples of acute triangles:

Practice Problems:

1. Identify whether the following triangles are acute triangles or not:
   • a) A triangle with angles measuring 60°, 60°, and 60°
   • b) A triangle with angles measuring 45°, 45°, and 90°
   • c) A triangle with angles measuring 30°, 60°, and 90°
2. Find the measure of the third angle in each of the following acute triangles:
   • a) Angle A = 30°, Angle B = 60°
   • b) Angle A = 45°, Angle B = 50°
3. Given the side lengths of an acute triangle as 3 cm, 4 cm, and 5 cm, find the measures of the angles.