Double-Angle Formulas
Select your language EnglishSpanish Let α be an angle. The double-angle (2α) trigonometric ratios can be expressed as a function of the trigonometric ratios of the angle α, that is, the double-angle formulas: Double-Angle...
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Area of a Right Triangle
Select your language EnglishSpanish The right triangle has a right angle (90°), so its height coincides with one of its sides (a) and its base with the other side (b). The area of a...
Centroid of a Triangle
Select your language EnglishSpanish The centroid of a triangle (or barycenter of a triangle) G is the point where the three medians of the triangle meet. The medians of a triangle are the line...
Points, Lines, and Circles Associated with a Triangle
Select your language EnglishSpanish Every triangle has lines (also called cevians) and points that determine a number of important elements. There are many different constructions that find a special point associated with a triangle,...
Thales’ Theorem
Select your language EnglishSpanish There are several theorems that are attributed to Thales of Miletus, we are going to focus especially on two of them: Thales’ Theorem Thales’ Theorem is a special case of...
Similar triangles
Select your language EnglishSpanish In Euclidean geometry, two objects are similar if they are the same shape, regardless of their size. Two triangles are similar if, and only if, their angles are congruent (equal)...
Equilateral triangle
Select your language EnglishSpanish The equilateral triangle is the regular polygon simplest. Its three sides are equal. Therefore, their angles are also the three equal. Since all angles are equal and the angles are...
Trigonometric ratios and Trigonometric Functions
Select your language EnglishSpanish Trigonometric ratios are defined as the ratios of the sides of a right triangle. There are six trigonometric ratios in total: sine, cosine, tangent, and their reciprocals, cosecant, secant and...
Sum and Difference Identities and Formulas
Select your language EnglishSpanish Angle sum and difference identities express trigonometric functions of sums of angles α ± β in terms of functions of α and β. Using the sum and difference formulas allows us to...
Area of a Triangle Using the Base and Height
Select your language EnglishSpanish The area of any triangle can be calculated by knowing one side and the height (or altitude), associated with that side. This side serves as the base. In fact the...