bassvorti.blogg.se

Tick marks on the edge of a triangle are a common notation that reflects the length of the side, where the same number of ticks means equal length.

When none of the sides of a triangle have equal lengths, it is referred to as scalene, as depicted below.

For example, a triangle in which all three sides have equal lengths is called an equilateral triangle while a triangle in which two sides have equal lengths is called isosceles. Furthermore, triangles tend to be described based on the length of their sides, as well as their internal angles. Hence, a triangle with vertices a, b, and c is typically denoted as Δabc. A triangle is usually referred to by its vertices. A vertex is a point where two or more curves, lines, or edges meet in the case of a triangle, the three vertices are joined by three line segments called edges. When radians are selected as the angle unit, it can take values such as pi/2, pi/4, etc.Ī triangle is a polygon that has three vertices. Please provide 3 values including at least one side to the following 6 fields, and click the "Calculate" button. Triangles △ACD and △BCD both have legs of length, and hypotenuse s.Home / math / triangle calculator Triangle Calculator Special trianglesĪn altitude divides an equilateral triangle into two 30°-60°-90° triangles.Īltitude CD divides equilateral triangle △ABC into two 30°-60°-90° triangles. The same relationships would be found for altitudes drawn from vertices A and C. Side AC reflects onto itself when reflecting across the altitude. Side AB reflects across the altitude to side BC. Refer to altitude BD extending from vertex B in the diagram below: The three altitudes of an equilateral triangle are also lines of symmetry. Lines of symmetry of an equilateral triangle Since the altitudes are the angle bisectors, medians, and perpendicular bisectors, point G is the orthocenter, incenter, centroid, and circumcenter of the triangle. The three altitudes extending from the vertices A, B, and C of △ABC above intersect at point G.

The three altitudes of an equilateral triangle intersect at a single point. Altitudes of equilateral trianglesĪn altitude of an equilateral triangle is also an angle bisector, median, and perpendicular bisector. Triangle △ABC and triangle △PQR are equiangular so, △ABC ~ △PQR. Since an equilateral triangle is also an equiangular triangle, it is a regular polygon. Properties of equilateral triangles Equilateral triangles are regular polygons This is true for any equilateral triangle. Since the sum of the angles for any triangle is 180°: Also, since DE≅DF, ∠E≅∠F, so by the transitive property, ∠D≅∠E≅∠F. Since DE≅EF, the base angles, ∠D and ∠F, are congruent. Recall from above that an equilateral triangle is also an isosceles triangle. In an isosceles triangle, the base angles are congruent. Angle measuresĪn equilateral triangle is also called an equiangular triangle since its three angles are equal to 60°. △ABC is an equilateral triangle since AB≅AC≅BC.Īn isosceles triangle has at least two equal sides, so an equilateral triangle is also an isosceles triangle.