![]() Next, look at the right half of the triangle.This “bisects” the equilateral triangle into two halves. First, draw a dotted line from the top corner of the triangle to the opposite side (the dotted line and the opposite side should meet at a 90 degree angle).To prove this, we take the following steps: The height h of an equilateral triangle with side length x is given by the formula: How To Find The Height Of An Equilateral Triangle This means that a right triangle cannot be equilateral (a 90 degree angle in a right triangle is inconsistent with three 60 degree angles in an equilateral triangle). As we mentioned before, a right triangle can never be equilateral.Ī right triangle has perpendicular sides (which meet at the 90 degree angle). When two sides of a triangle are perpendicular, they meet at a 90 degree angle, and so we have a right triangle. Likewise, any triangle with two perpendicular sides cannot be equilateral. So, no pair of sides can be perpendicular, since perpendicular sides would have to meet at a 90 degree angle. Remember: any pair of sides in an equilateral triangle will meet at a 60 degree angle. Does An Equilateral Triangle Have Perpendicular Sides?Īn equilateral triangle never has perpendicular sides. This would result in a polygon with 4 or more sides, which is not a triangle. We would need to add and least two more line segments to the figure to “close” the shape. Two sides that are parallel would never intersect, so they would never meet to form an angle. Likewise, any polygon with two parallel sides is not a triangle. Remember: any pair of sides in an equilateral triangle will meet (at a 60 degree angle), so any pair of sides cannot be parallel. Does An Equilateral Triangle Have Parallel Sides?Īn equilateral triangle never has parallel sides. ![]() The measure of each exterior angle is 360 / 3 = 120 degrees. The measure of each interior angle is 180 / 3 = 60 degrees. Since all three sides are the same length, it follows that all three angles have the same measure.Īn equilateral triangle is a regular polygon with n = 3 sides, interior angles of 60 degrees, and exterior angles of 120 degrees.įor an equilateral triangle, we have a regular polygon with 3 sides (n = 3). Do Equilateral Triangles Have Equal Angles?Įquilateral triangles do have equal angles. This gives equilateral certain special properties, which we will discuss below. All About Equilateral TrianglesĪn equilateral triangle is a triangle where all three sides have the same length. We’ll also answer some common questions about this specific type of triangle. In this article, we’ll talk about equilateral triangles and their sides, angles, height, and area. Remember that an equilateral triangle is a special type of regular polygon: one with n = 3 sides, interior angles of 60 degrees, and exterior angle of 120 degrees. Any pair of equilateral triangles is similar, but not necessarily congruent. An equilateral triangle is isosceles and acute, but never scalene or right. So, what do you need to know about equilateral triangles? Equilateral triangles have 3 sides of the same length and 3 angles with the same measure (60 degrees), but no parallel or perpendicular sides. We can also calculate their heights and areas once we know the formulas. Equilateral triangles are common in geometry courses, so it pays to know about their sides and angles.
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