Is every equilateral triangle acute?
Understand the Problem
The question is asking whether all angles in an equilateral triangle are acute angles. An equilateral triangle is defined as having all three sides of equal length and all three angles equal to each other. Since the sum of the angles in any triangle is 180 degrees, we can deduce that each angle in an equilateral triangle measures 60 degrees, which is an acute angle. Therefore, the answer would be yes.
Answer
Yes, all angles in an equilateral triangle are acute angles.
Answer for screen readers
Yes, all angles in an equilateral triangle are acute angles.
Steps to Solve
- Understanding the Angles of a Triangle
In any triangle, the sum of the interior angles is always $180$ degrees.
- Calculating the Angles of an Equilateral Triangle
Since an equilateral triangle has all three angles equal, we can find the measure of each angle by dividing the total sum of the angles by the number of angles:
$$ \text{Angle} = \frac{180}{3} = 60 \text{ degrees} $$
- Determining if Angles are Acute
An acute angle is defined as an angle that is less than $90$ degrees. Since $60$ degrees is less than $90$ degrees, each angle in the equilateral triangle is indeed an acute angle.
Yes, all angles in an equilateral triangle are acute angles.
More Information
An equilateral triangle is a special type of triangle where not only the angles are equal but the lengths of the sides are also equal. This is consistent across all equilateral triangles, making their angles always $60$ degrees.
Tips
- A common mistake is confusing the angles of an equilateral triangle with those of other types of triangles. Ensure that the properties of equilateral triangles are applied correctly.
