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Properties of Triangle (Propiedades de los triangulos) Lizeth Vega

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Properties of Triangle (Propiedades de los triangulos) Lizeth Vega

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Understanding the properties of triangle is crucial for geometry.

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GEOMETRIA PLANA UNAD
GEOMETRIA PLANA UNAD
Colombia

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Properties of Triangle (Propiedades de los triangulos) Lizeth Vega
 

Properties of Triangle (Propiedades de los triangulos) Lizeth VegaOnline version

Understanding the properties of triangle is crucial for geometry.

by GEOMETRIA PLANA UNAD
1

What is Angle Sum Property of a Triangle (¿Qué es la propiedad de suma de ángulos de un triángulo?)

The most fundamental property of triangle is that the sum of all interior angles always equals 180 degrees. This holds true for every triangle, regardless of type—acute, obtuse, right, equilateral, isosceles, or scalene.

Mathematically expressed: ∠A + ∠B + ∠C = 180°

(La propiedad más fundamental del triángulo es que la suma de todos los ángulos interiores siempre es igual a 180 grados. Esto es cierto para cualquier triángulo, independientemente del tipo: agudo, obtuso, derecho, equilátero, isóscele o escaleno.

Expresado matemáticamente: ∠A + ∠B + ∠C = 180°)

2

What is Angle Sum Property of a Triangle (¿Qué es la propiedad de suma de ángulos de un triángulo?)

This fundamental rule of the triangle appears in several ways:

  • Direct application: When two angles are given, you can easily find the third. (Aplicación directa: Cuando se dan dos ángulos, puedes encontrar fácilmente el tercero)
  • Algebraic expressions: GMAT often presents angles using variables and expressions. (Expresiones algebraicas: El GMAT suele presentar ángulos usando variables y expresiones.)
3

Interior Angle Properties (Propiedades del ángulo interior)

Interior Angle Properties:

  • Sum Property: The sum of interior angles always equals 180°
  • Complementary Angles: In a right triangle, the two non-right angles sum to 90°
  • Isosceles Triangle: If two sides are equal, then the angles opposite those sides are equal
  • Equilateral Triangle: All interior angles equal 60°


(Propiedades del ángulo interior:

  • Propiedad de suma: La suma de los ángulos interiores siempre es igual a 180°
  • Ángulos complementarios: En un triángulo rectángulo, los dos ángulos no rectos suman 90°
  • Triángulo isósceles: Si dos lados son iguales, entonces los ángulos opuestos a esos lados son iguales
  • Triángulo equilátero: Todos los ángulos interiores son 60°)
4

Exterior Angle Properties (Propiedades del ángulo exterior)

  • An exterior angle of a triangle equals the sum of the two non-adjacent interior angles
  • Mathematically: ∠exterior = ∠non-adjacent1 + ∠non-adjacent2
  • The sum of exterior angles (one at each vertex) equals 360°


  • (Un ángulo exterior de un triángulo es igual a la suma de los dos ángulos interiores no adyacentes
  • Matemáticamente: ∠exterior = ∠no adyacente1 + ∠no adyacente2
  • La suma de los ángulos exteriores (uno en cada vértice) es igual a 360°)
5

Angle-Side Relationship (Relación de ángulo)

Side-Angle Relationship

  • The largest angle is opposite to the longest side
  • The smallest angle is opposite to the shortest side
  • In general, sides and their opposite angles have the same relative ordering


Relación de ángulo lateral

  • El ángulo más grande es opuesto al lado más largo
  • El ángulo más pequeño es opuesto al lado más corto
  • En general, los lados y sus ángulos opuestos tienen el mismo orden relativo
6

Angle-Side Relationship (Relación de ángulo)

Equal Sides and Angles

  • If two sides are equal (isosceles triangle), the angles opposite these sides are equal
  • If all sides are equal (equilateral), all angles are equal (60° each)
  • Conversely, if two angles are equal, the sides opposite them are equal


(Lados y ángulos iguales

  • Si dos lados son iguales (triángulo isósceles), los ángulos opuestos a estos lados son iguales
  • Si todos los lados son iguales (equiláteros), todos los ángulos son iguales (60° cada uno)
  • Por el contrario, si dos ángulos son iguales, los lados opuestos a ellos son iguales)
 
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