Acute Triangle Study Guide

Definition:

Properties:

• All three angles are acute angles (<90 degrees).
• The sum of the three angles is less than 180 degrees.
• It can be scalene, isosceles, or equilateral.
• It is not a right triangle or an obtuse triangle.

Examples:

Here are some examples of acute triangles:

1. Scalene Acute Triangle: A triangle with all three sides of different lengths and all angles less than 90 degrees.
2. Isosceles Acute Triangle: A triangle with two sides of the same length and all angles less than 90 degrees.
3. Equilateral Acute Triangle: A triangle with all three sides of the same length and all angles less than 90 degrees.

Formula:

There is no specific formula for finding the properties of an acute triangle, but it's important to remember the sum of the interior angles of any triangle is always 180 degrees.

Practice Problems:

Here are some practice problems to test your understanding:

1. Find the measures of the angles in an acute triangle with angles measuring 30°, 60°, and 80°.
2. Determine whether the following triangles are acute triangles:
   • a) A triangle with angles measuring 45°, 45°, and 90°.
   • b) A triangle with angles measuring 70°, 100°, and 10°.

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