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Acute triangles are a type of triangle that have all three of their interior angles measuring less than 90 degrees. In other words, all three angles of an acute triangle are acute angles. These triangles are known for their sharp, pointed appearance, and they have a number of important properties and characteristics that make them unique among the different types of triangles.

DEFINITIONS

• Triangle: A triangle is a three-sided polygon with three straight sides.
• Acute angle: An acute angle is an angle that measures less than 90 degrees.
• Acute triangle: An acute triangle is a triangle that has all three of its interior angles measuring less than 90 degrees.

EXAMPLES

1. Right triangle: A right triangle is a triangle that has one of its angles measuring exactly 90 degrees. This angle is known as the right angle, and it is denoted by a small square symbol. The other two angles of a right triangle are acute angles, which means that right triangles are also acute triangles.
2. Obtuse triangle: An obtuse triangle is a triangle that has one of its angles measuring more than 90 degrees. The other two angles of an obtuse triangle are both acute angles, which means that obtuse triangles are not acute triangles.
3. Isosceles triangle: An isosceles triangle is a triangle that has two sides with the same length. The two equal sides are called the base of the triangle, and the third side is called the altitude. An isosceles triangle can be acute or obtuse, depending on the measure of its angles.
4. Equilateral triangle: An equilateral triangle is a triangle that has all three of its sides with the same length. The three equal sides of an equilateral triangle are called the base of the triangle, and the three angles are all 60 degrees. An equilateral triangle is always an acute triangle.
5. Scalene triangle: A scalene triangle is a triangle that has no sides with the same length. The three sides of a scalene triangle are all different lengths, and the three angles are also all different. A scalene triangle can be acute, right, or obtuse, depending on the measure of its angles.

QUIZ

1. Which of the following is not an acute triangle? a. Right triangle b. Obtuse triangle c. Isosceles triangle d. Equilateral triangle
2. Which of the following is not a property of an acute triangle? a. All three sides are of equal length b. All three angles are acute c. One angle is a right angle d. One angle is an obtuse angle
3. Which of the following triangles is always an acute triangle? a. Right triangle b. Obtuse triangle c. Isosceles triangle d. Equilateral triangle
4. What is the sum of the measures of the angles in an acute triangle? a. 180 degrees b. 90 degrees c. 270 degrees d. 360 degrees
5. Can an acute triangle be a scalene triangle? a. Yes b. No
6. Can an acute triangle be an isosceles triangle? a. Yes b. No
7. Can an acute triangle be an equilateral triangle? a. Yes b. No
8. Can an acute triangle have one angle measuring more than 90 degrees? a. Yes b. No