mathematical definition of a triangle
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triangle triangle. n. 1. (Mathematics) geometry a three-sided polygon that can be classified by angle, as in an acute triangle, or by side, as in an equilateral triangle. Sum of interior angles: 180°; area: base × height. 2. any object shaped like a triangle. 3. any situation involving three parties or points of view. See also eternal triangle. 4. (Instruments) music a percussion instrument consisting of a sonorous metal bar bent into a triangular shape, beaten with a metal stick.
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Right triangle Right triangle. A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90- degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus).
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- Examples 1. A triangle is a three-sided polygon. A polygon is a closed figure in a plane that is made up of segments called sides that intersect only at their endpoints, called vertices. 2. Triangle ABC, written ∆ABC, has the following parts.
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The Geometry of Triangles The Pythagorean Theorem: This formula is for right triangles only!The sides, a and b, of a right triangle are called the legs, and the side that is opposite to the right (90 degree) angle, c, is called the hypotenuse. This formula will help you find the length of either a, b or c, if you are given the lengths of the other two.
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- Boils and carbuncles. Overview. Boil A boil is a painful, pus-filled bump under your skin — the result of a bacterial infection of one or more hair follicles. Carbuncle A carbuncle is a cluster of boils — painful, pus-filled bumps — that form a connected area of infection under the skin.
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Degrees: Circles, Triangles, Rectangles, Squares A triangle is a closed figure that has three sides and three angles. The sum of the three angles of every triangle always equals 180° . A right triangle always has one angle equal to 90° and two angles whose sum is 90° , making a total of 180° . Rectangles. A rectangle is a four sided shape with four right angles (90° ). The sides across from each other are always the same length and always parallel to each other. The four angles add up to a total of 360° .
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Triangle Inequality Theorem Triangle Inequality Theorem. In mathematics, here we will study about the Triangle Inequality Theorem. Before solving the theorem first it is necessary to know about the triangle. Triangle is a three line paked shape that is linked end-to-end with each other.
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"Full text of ""A treatise on the higher plane curves: intended as a sequel to A treatise on conic sections""" IN MATH: 1. n. in a right triangle, the ratio of the length of the adjacent side to the length of the opposite side: the reciprocal of the tangent. 2. n. a trigonometric function defined for all angles except + 180°, - 180°, + 360°, - 360°, + 540°, - 540°, + 720°, - 720°, etc. EX. cot (45°) = 1.
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Altitude (triangle) In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle).
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Triangle Condition on the sides. The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.
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Triangles A triangle that has one right angle is called a right triangle. A triangle that has one obtuse angle is called an obtuse triangle. When a triangle has three congruent sides, we call the triangle an equilateral triangle. We mark the congruent sides by a slash mark. The angles in an equilateral triangle are always 60°. When a triangle has two congruent sides it is called an isosceles triangle. The angles opposite to the two sides of the same length are congruent. A triangle without any congruent sides or angles is called a scalene triangle. When two triangles are congruent it means that they have the same size and shape. This means that they have the same angles.
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Degrees: Circles, Triangles, Rectangles, Squares A triangle is a closed figure that has three sides and three angles. The sum of the three angles of every triangle always equals 180° . A right triangle always has one angle equal to 90° and two angles whose sum is 90° , making a total of 180° . A rectangle is a four sided shape. with four right angles (90° ).
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Geometry/Right Triangles and Pythagorean Theorem Geometry/Right Triangles and Pythagorean Theorem - Right triangles. 1  Right triangles are triangles in which one of the interior angles is 90o. A 90o angle is called a right angle. 2  The side opposite of the right angle is called the hypotenuse. The sides adjacent to the right angle are the legs.
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Triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted △ A B C {\displaystyle \triangle ABC} .
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Equilateral Triangle Equilateral Triangle. An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a regular triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal angles.
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Triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted △ A B C {\displaystyle \triangle ABC}.
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Triangle 1 An equilateral triangle is also a regular polygon with all angles 60°. 2  In an isosceles triangle, at least two sides are equal in length. 3  An isosceles triangle also has two equal angles: the angles opposite the two equal sides. 4  In a scalene triangle, all sides and internal angles are different from one another.
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Triangle The altitude of a triangle is the perpendicular from the base to the opposite vertex. (The base may need to be extended). Since there are three possible bases, there are also three possible altitudes. The three altitudes intersect at a single point, called the orthocenter of the triangle.
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Triangle 1 Acute Triangle: A triangle measuring all its angles less than 90o is called acute triangle.A three-sided polygon with all its angles less than 90o is called acute triangle. 2  Obtuse Triangle: A triangle with one of its angle measuring more than 90o is called obtuse triangle.
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Triangle Triangles can be classified according to the relative lengths of their sides: 1  In an equilateral triangle, all sides are the same length. 2  An equilateral triangle is also a regular polygon with all angles 60°. 3  In an isosceles triangle, at least two sides are equal in length.
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Medians and Altitudes in Triangles Medians. Median: The line segment that joins a vertex and the midpoint of the opposite side (of a triangle). Example 1: Draw the median for below. Solution: From the definition, we need to locate the midpoint of.
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What is an Equilateral Triangle? - Definition, Properties & Formula Perimeter of an Equilateral Triangle. The perimeter of any shape is the sum of the lengths of all its sides. Since an equilateral triangle's sides are all of equal length, we only need the length of one side to calculate its perimeter. Once we have the length of one side, we would add it to itself three times to find the triangle's perimeter.
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What is a Polygon? - Definition, Shapes & Angles Definition of a Polygon. A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides. So, any shape that can be drawn by connecting three straight lines is called a triangle, and any shape that can be drawn by connecting four straight lines is called a quadrilateral. All of these shapes are polygons.
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Triangle Altitude Theorem Altitude of a Triangle Tutorial. An Altitude of a Triangle is defined as the line drawn from a vertex perpendicular to the opposite side - AHa, BHb and CHc in the below figure. Vertex is a point of a triangle where two line segments meet. For example, the points A, B and C in the below figure.
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- Triangle Definition. Triangle is a closed figure formed by three sides and three angles. Triangle ABC shown above is formed by the three sides (line segments) AB, BC and CA. The three angles A, B and C are formed at the pairwise intersections of these sides.
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What is a Polygon? - Definition, Shapes & Angles Definition of a Polygon. A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides.