Definition of equilateral triangle

Since equi- means "equal", the meaning of equilateral is easy to guess from its roots. The word is mostly used in geometry. The standard polygons (many-sided geometrical shapes)—the pentagon, hexagon, octagon, etc.—are assumed to be equilateral if we don't say otherwise; an equilateral rectangle has the special name square. But triangles are particularly important, and many triangles are not equal-sided. The standard polyhedrons (many-sided solids) are also equilateral. Most common is the cube, all of whose sides are square. The tetrahedron has four triangular sides and thus is a pyramid with a triangular base, unlike the pyramids of Egypt with their square bases. Recent Examples on the Web Waldo has floppy ears shaped like perfect equilateral triangles and feet too big for his lanky body, which continues to grow. — Gemma Tarlach, Discover Magazine, 25 Nov. 2014 The set includes 48 regular squares, eight large squares, eight thick-sided squares, eight squares that look like windowpanes, 16 small and 16 large equilateral triangles plus 16 isosceles triangles. — Jessica Hartshorn, Good Housekeeping, 19 Dec. 2022 The equilateral cross with its legs bent at right angles is a millennia-old sacred symbol in Hinduism, Buddhism and Jainism that represents peace and good fortune. — Arkansas Online, 28 Nov. 2022 The equilateral cross with its legs bent at right angles is a millennia-old sacred symbol in Hinduism, Buddhism, and Jainism that represents peace and good fortune. — Deepa ...

Similar Triangles Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different. In general, similar triangles are different from congruent triangles. There are various methods by which we can find if two triangles are similar or not. Let us learn more about similar triangles and their properties along with a few solved examples. 1. 2. 3. 4. 5. 6. 7. What are Similar Triangles? Similar triangles are the triangles that look similar to each other but their sizes might not be exactly the same. Two objects can be said similar if they have the same shape but might vary in size. That means similar Similar Triangles Definition Two triangles will be similar if the angles are equal ( • All corresponding angle pairs of triangles are equal. • All corresponding sides of triangles are proportional. We use the "∼" symbol to represent the similarity. So, if two triangles are similar, we show it as △QPR ∼ △XYZ Similar Triangles Examples Similar triangles are triangles for which the corresponding angle pairs are equal. That means equiangular triangles are similar. Therefore, all equilateral triangles are examples of similar triangles. The following image shows similar triangles, but we must notice that their sizes are different. Similar Triangles Formulas In the previous section, we saw there are two conditions using which we can verify if the given s...

• Math Lessons • Prehistoric Mathematics • Sumerian/Babylonian Mathematics • Egyptian Mathematics • Greek Mathematics • Pythagoras • Plato • Hellenistic Mathematics • Euclid • Archimedes • Diophantus • Roman Mathematics • Mayan Mathematics • Chinese Mathematics • Indian Mathematics • Brahmagupta • Madhava • Islamic Mathematics • Al-Khwarizmi • Medieval European Mathematics • Fibonacci • 16th Century Mathematics • Tartaglia, Cardano and Ferrari • 17th Century Mathematics • Descartes • Fermat • Pascal • Newton • Leibniz • 18th Century Mathematics • Bernoulli Brothers • Euler • 19th Century Mathematics • Galois • Gauss • Bolyai and Lobachevsky • Riemann • Boole • Cantor • Poincaré • 20th Century Mathematics • Hardy and Ramanujan • Russell and Whitehead • Hilbert • Godel • Turing • Weil • Cohen • Robinson and Matiyasevich Definition An equilateral triangle has sides of the same length, making it a special kind of triangle in geometry. Three right angles are also equal in size since their opposite sides are also equal in length. Therefore, it is also termed an equiangular triangle, in which each angle measures 60 degrees. It is possible to calculate the area, perimeter, and height of an equilateral triangle in the same way that these measurements can be calculated for other triangles. What Is a Triangle With Equilateral Sides? Additionally, all three of the triangle’s angles add up to a total of sixty degrees and are congruent. The total angle equals 180 degrees when all three ...

Altitude of a Triangle The altitude of a triangle is a perpendicular that is drawn from the vertex of a triangle to the opposite side. Since there are three sides in a triangle, three altitudes can be drawn in it. Different triangles have different kinds of altitudes. The altitude of a triangle which is also called its height is used in calculating the area of a triangle and is denoted by the letter 'h'. 1. 2. 3. 4. 5. Altitude of a Triangle Properties The altitudes of various types of triangles have some properties that are specific to certain triangles. They are as follows: • A triangle can have three altitudes. • The altitudes can be inside or outside the triangle, depending on the type of triangle. • The altitude makes an angle of 90° to the side opposite to it. • The point of intersection of the three altitudes of a triangle is called the orthocenter of the triangle. Altitude of a Triangle Formula The formula for the altitude of a triangle can be derived from the basic formula for the area of a triangle which is: Area = 1/2 × base × height, where the height represents the altitude. Using this formula, we can derive the altitude formula which will be, Altitude of triangle = (2 × Area)/base. How to Find the Altitude of a Triangle? Let us learn how to find out the altitude of a scalene triangle, equilateral triangle, right triangle, and isosceles triangle. Altitude Formula The important formulas for the altitude of a triangle are summed up in the following table. The fol...

An equilateral triangle is a triangle that has all sides of equal lengths. For example, a triangle that has all its sides 10 cm long is an equilateral triangle. Since all three sides are equal, the three interior angles also have the same measure. Thus, we can also think of an equilateral triangle as a triangle that has three 60-degree angles. Here, we will look at a definition of equilateral triangles. Also, we will learn about the fundamental properties of these triangles and we will look at some of their most important formulas. Finally, we will use these formulas to solve some problems. Definition of an equilateral triangle As we mentioned in the introduction, an equilateral triangle is a triangle that has all sides of equal lengths. Also, the three interior angles of an equilateral triangle are also congruent and equal to 60 degrees. The following is a diagram of an equilateral triangle: Important characteristics of equilateral triangles Equilateral triangles have the following fundamental characteristics: • An equilateral triangle has all its sides with equal length. • All the internal sides of an equilateral triangle measure 60°. • The equilateral triangle is a regular polygon with three sides. • A triangle is equilateral only if the circumcenters of the three smallest triangles have the same distance from the centroid. • A triangle is equilateral only if the three smallest triangles have the same perimeter. • The orthocenter and centroid of the triangle are the sam...

The shortest side is the one opposite the smallest angle. If the angle you already know is the shortest one, then the shortest side is opposite it. However, if the angle you already know is the medium one, then the shortest side is adjacent to it. The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle. Trigonometry is very useful in any type of physics, engineering, meteorology, navigation, etc... (Wherever geometry is useful, trig is almost certain to also be useful). Trig isn't for everyone, however if little billy wants to calculate how tall a building is without producing the world's longest tape measure, he's gonna need some trig. The name sine (from what i know) comes from the latin word sinus, meaning hole or cavity, basically translation after translation of the word we ended with hole, which turned into sinus, sine for short (I may be wrong, but that is what I remember). The name cosine comes from the fact that sine and cosine are co-functions, (due to the fact that sin(x-90)=cosx. Tangent is not as easy to explain, it has to do with geometry and tangent lines. Trigonometry is part of the standard high school curriculum, but it's not an essential subject for nothing. Many career choices involve studying trigonometry, especially STEM fields such as science, engineering, or technology. In the end, it depends on you and your career choice. Because, if anything, trigonometry is very useful for...