Triangles
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This document discusses the key properties and types of triangles. It defines what a triangle is, noting that it has 3 sides, 3 angles, and 3 vertices. It then describes the different shapes of triangles including scalene, equilateral, and isosceles triangles. The document also outlines the different types of triangles based on angle measures, including acute, right, and obtuse triangles. Finally, it provides formulas for calculating the area of a triangle.
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This document defines and describes different types of triangles based on side lengths and angle measures. It explains that a triangle is a three-sided closed shape, and triangles can be named as equilateral, isosceles, or scalene based on equal or unequal side lengths, or as acute, right, or obtuse based on angle measures less than, equal to, or greater than 90 degrees.
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There are two main ways to classify triangles: by the lengths of their sides and by the measure of their angles. For side classification, an equilateral triangle has all three sides the same length, an isosceles triangle has two sides of equal length, and a scalene triangle has all sides of different lengths. For angle classification, an acute triangle has all angles less than 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and a right triangle has one 90 degree angle. Triangles can be proven congruent through various postulates and theorems including SSS, SAS, ASA, AAS, and RHS which relate congruent sides and angles.
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This document defines and provides examples of six types of triangles: scalene triangles which have no equal sides; isosceles triangles which have two equal sides; equilateral triangles which have three equal sides; right triangles which have one 90 degree angle; obtuse triangles which have one angle greater than 90 degrees; and acute triangles where all angles are less than 90 degrees.
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The document discusses the classification of triangles based on the lengths of their sides and measures of their angles. Triangles can be classified as scalene, isosceles, or equilateral depending on whether they have no sides, two sides, or all three sides of equal length. They can also be classified as acute, right, obtuse, or equiangular based on the measures of their angles. Several examples of different types of triangles are provided.
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The document discusses classifying triangles based on their sides and angles. It explains that triangles can be equilateral, isosceles, or scalene based on their side lengths. Triangles can also be acute, obtuse, or right based on their angle measures. The document provides examples of finding the measure of the third angle of a triangle when two angles are given.
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There are two main ways to classify triangles: by the lengths of their sides and by the measure of their angles. For side classification, an equilateral triangle has all three sides the same length, an isosceles triangle has two sides of equal length, and a scalene triangle has all sides of different lengths. For angle classification, an acute triangle has all angles less than 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and a right triangle has one 90 degree angle. Triangles can be proven congruent through various postulates and theorems including SSS, SAS, ASA, AAS, and RHS which relate congruent sides and angles.
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This document defines and provides examples of six types of triangles: scalene triangles which have no equal sides; isosceles triangles which have two equal sides; equilateral triangles which have three equal sides; right triangles which have one 90 degree angle; obtuse triangles which have one angle greater than 90 degrees; and acute triangles where all angles are less than 90 degrees.
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The document discusses the classification of triangles based on the lengths of their sides and measures of their angles. Triangles can be classified as scalene, isosceles, or equilateral depending on whether they have no sides, two sides, or all three sides of equal length. They can also be classified as acute, right, obtuse, or equiangular based on the measures of their angles. Several examples of different types of triangles are provided.
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This document discusses two ways to classify triangles: by their sides and by their angles. Triangles can be classified by their sides as scalene if no sides are the same length or isosceles if at least two sides are the same length. Triangles can be classified by their angles as acute if all angles are less than 90 degrees, right if one angle is 90 degrees, or obtuse if one angle is greater than 90 degrees. Examples are given of classifying triangles under each system.
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A triangle is a 3-sided polygon with three sides, three vertices, and three angles. Triangles can be categorized based on their side lengths as either equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal). They can also be categorized based on their angle measures as either acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), or right (one angle of 90 degrees). The study of triangles, known as triangle geometry, contains many beautiful theorems and relationships.
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IDENTIFYING AND DESCRIBING TRIANGLES ACCORDING TO SIDES AND ANGLE
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This document discusses various theorems and properties related to triangles. It explains the Basic Proportionality Theorem, also known as Thales' Theorem, which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. It also covers similarity criteria like AAA, SSA, and SSS. The Area Theorem demonstrates that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Additionally, it proves Pythagoras' Theorem, which relates the sides of a right triangle, and its converse. In summary, the document outlines key triangle theorems regarding proportional division, similarity, areas, and the Pythagorean relationship between sides.
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This document provides an overview of triangles, including definitions, types, properties, secondary parts, congruency, and area calculations. It defines a triangle as a 3-sided polygon with three angles and vertices. Triangles are classified by side lengths as equilateral, isosceles, or scalene, and by angle measures as acute, obtuse, or right. Key properties discussed include the angle sum theorem, exterior angle theorem, and Pythagorean theorem. Secondary parts like medians, altitudes, perpendicular bisectors, and angle bisectors are also defined. Tests for triangle congruency such as SSS, SAS, ASA, and RHS are outlined. Formulas are provided for calculating the areas of
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This document defines and classifies triangles based on the lengths of their sides and the measures of their interior angles. It explains that triangles can be equilateral, isosceles, or scalene based on whether their sides are all equal, two sides are equal, or all sides are unequal. Triangles can also be right, obtuse, or acute based on whether they have a 90 degree angle, an angle over 90 degrees, or all angles under 90 degrees. The document provides examples and diagrams to illustrate different types of triangles.
Introduction of triangle for class 8th 10th
This document discusses different shapes and classifications of triangles. It defines squares as having all equal sides that meet at right angles. It notes that all squares and circles have the same shape, while triangles can have different shapes. Triangles are classified based on their sides as equilateral (all equal sides), isosceles (two equal sides), or scalene (no equal sides). They are also classified based on their angles as right, acute, obtuse, or reflex. The document provides definitions for these angle classifications. It concludes with summaries of congruent and similar figures.
Geometry of shape and size
This document defines and describes different types of triangles based on side lengths and angles. It explains that a triangle has three sides and three angles that always sum to 180 degrees. Scalene triangles have three unequal sides, isosceles triangles have two equal sides, and equilateral triangles have three equal sides. Right triangles contain one 90 degree angle. The document provides an example of using the triangle angle sum rule to calculate the measure of an unknown angle given the measures of the other two angles.
Triangle
This document discusses how triangles can be classified into different types based on the length of their sides or the measure of their angles. Triangles are classified based on side length as equilateral, isosceles, or scalene, and based on angle measure as acute, right, obtuse, or equiangular.
Triangles
Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.
Triangle
The document discusses how triangles can be classified into different types based on the length of their sides or the measure of their angles. Triangles can be equilateral, isosceles, or scalene depending on whether their sides are all the same length, at least two sides are the same length, or no sides are the same length, respectively. Additionally, triangles can be acute, right, obtuse, or equiangular depending on whether their angles are all acute, one angle is right, one angle is obtuse, or all angles have the same measure.
Triangles
Triangles can be classified based on side lengths as equilateral, isosceles, or scalene triangles. They can also be classified based on angles as acute, obtuse, or right triangles. The three main properties of triangles are the angle sum property, exterior angle property, and Pythagorean theorem. Congruent triangles can be proven using the SSS, SAS, ASA, AAS, or RHS criteria which compare corresponding sides and angles. Important parts of a triangle include the median, altitude, angle bisector, and perpendicular bisector. The triangle inequality states that the sum of any two sides must be greater than the third side. Important points related to triangles are the incenter, circumcenter,
Triangle
The document discusses properties of triangles. It states that a triangle has three sides and three angles, the sum of the angles is always 180 degrees, and the exterior angles always add up to 360 degrees. It also notes that the sum of any two side lengths is greater than the third side, and that the line segment joining the midpoints of any two sides is parallel to the third side.
Geom 4point1
This document provides definitions and properties related to triangles:
- It defines different types of triangles based on sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse).
- It identifies key parts of triangles like vertices, adjacent/opposite sides, hypotenuse, legs, and base.
- It describes interior and exterior angles and states the Triangle Sum Theorem that the interior angles sum to 180 degrees.
- The Exterior Angle Theorem and corollary relating right triangles are also presented.
Present.julie
The document defines and describes the different types of triangles based on their angles and sides. It states that a triangle is a three-sided polygon with three angles and vertices. Triangles are categorized as being right, acute, or obtuse angled based on whether they have one 90 degree angle, all angles less than 90 degrees, or one angle greater than 90 degrees. They are also defined as being scalene, isosceles, or equilateral based on whether their sides are all different lengths, two sides are the same length, or all three sides are the same length respectively.
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Triangles
- 1. triangles Submitted to Mrs. Jyoti Arora
- 2. TRIANGLES
- 3. Basic learning A triangle has : 3 angles 3 sides 3 vertices It has 4 congruence The sum of its angles is always 180
- 5. Shapes of triangles 1. Scalene triangle : its all sides are different in length . 2. Equilateral triangle : its all sides are equal . 3. Isosceles triangle : its any 2 sides are equal.
- 6. Types of triangle Acute angled triangle : less than 90° Right angled triangle : Equal to 90° Obtuse angled triangle : Bigger than 90°
- 8. Different congruencies of triangle • SSS ( side , side , side ) : in this congruent form all the sides of triangle are equal . • SAS ( side , angle , side ) : in this congruent form 2 sides and 1 angle are equal . • ASA ( angle , side , angle ) : in this congruent form 2 angles and 1 side are equal . • AAA ( angle , angle , angle ) : in this congruent form all 3 angles are equal
- 9. AREA OF TRIANGLE • Formula : ½ base x height heron formula : √s ( s – a ) ( s – b ) ( s – c )