![]() 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. Theorem 27: Each angle of an equiangular triangle has a measure of 60°.Equilateral triangles are common in geometry courses, so it pays to know about their sides and angles. ![]() Equiangular triangle: A triangle having all angles of equal measure (Figure 7).īecause the sum of all the angles of a triangle is 180°, the following theorem is easily shown.Acute triangle: A triangle having all acute angles (less than 90°) in its interior (Figure 6).Obtuse triangle: A triangle having an obtuse angle (greater than 90° but less than 180°) in its interior.Right triangle: A triangle that has a right angle in its interior (Figure 4).The types of triangles classified by their angles include the following: Scalene triangle: A triangle with all three sides of different measures (Figure 3).Isosceles triangle: A triangle in which at least two sides have equal measure (Figure 2).In Figure 1, the slash marks indicate equal measure. Equilateral triangle: A triangle with all three sides equal in measure.The types of triangles classified by their sides are the following: All of each may be of different or the same sizes any two sides or angles may be of the same size there may be one distinctive angle. Triangles can be classified either according to their sides or according to their angles. Summary of Coordinate Geometry Formulas.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles. ![]()
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