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    una altura de un triangulo es un segmento de recta que va de un vértice y es perpendicular

    Santiago

    Chicos, ¿alguien sabe la respuesta?

    obtenga una altura de un triangulo es un segmento de recta que va de un vértice y es perpendicular de este sitio.

    Definiciones

    Definiciones

    Un triángulo es un polígono determinado por tres rectas que se cortan dos a dos en tres puntos (que no se encuentran alineados). Los puntos de intersección de las rectas son los vértices y los segmentos de recta determinados son los lados del triángulo. Dos lados contiguos forman uno de los ángulos interiores del triángulo.

    Los vértices se designan con las letras latinas mayúsculas. Los lados con las minúsculas. Los ángulos se representan con letras griegas, aunque también podemos referirnos a ellos con los nombres de los vértices.

    Se llama altura de un triángulo al segmento de recta que une un vértice del triángulo con el lado opuesto -o su prolongación- formando un ángulo recto. El lado opuesto es la base del triángulo. Las tres alturas se cortan en un punto llamado ortocentro.

    El segmento de recta que va de un vértice al punto medio del lado opuesto se llama mediana. Las tres medianas de un triángulo se cortan en un punto baricentro del triángulo.

    La mediatriz del lado de un triángulo es la recta perpendicular a dicho lado trazada por su punto medio. El triángulo tiene tres mediatrices, que se cortan en un punto O equidistante de los tres vértices llamado circuncentro. El circuncentro es el centro de una circunferencia que pasa por los tres vértices del triángulo.

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    La intersección de dos lados es un punto que se llama .

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    Para designar los se utilizan las letras latinas minúsculas.

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    El segmento de recta que une un vértice del triángulo con el lado opuesto formando

    un ángulo de 90º se llama .

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    Las medianas de un triángulo se cortan en un punto llamado .

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    Las se cortan en el circuncentro.

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    Obra colocada bajo licencia Creative Commons Attribution Non-commercial Share Alike 3.0 License

    fuente : mimosa.pntic.mec.es

    Altura (triángulo)

    Altura (triángulo)

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    Las tres alturas de un triángulo se cruzan en el ortocentro, que para un triángulo agudo se encuentra dentro del triángulo.

    En geometría plana, una altura de un triángulo es cada uno de los segmentos que une un vértice con un punto de su lado opuesto o de su prolongación y es perpendicular a dicho lado.

    Índice

    1 Términos y caracterizaciones

    2 Ortocentro 2.1 Propiedades

    2.2 Relación con círculos y cónicas

    2.3 Relación con otros centros, el círculo de nueve puntos

    3 Triángulo órtico

    4 Algunos teoremas y resultados adicionales

    4.1 Altura en función de los lados

    4.2 Teorema del inradio

    4.3 Teorema del circunradio

    4.4 Punto interior

    4.5 Punto general en una altura

    4.6 Casos especiales de triángulos

    4.6.1 Triángulo equilátero

    4.6.2 Triángulo rectángulo

    5 Véase también 6 Referencias 7 Bibliografía 8 Enlaces externos

    Términos y caracterizaciones[editar]

    El extremo de la altura que está en la base o su prolongación, se denomina de la altura. La longitud de la altura, a menudo simplemente llamada "la altura", es la distancia entre la base extendida y el vértice. El proceso de dibujar la altura desde el vértice al pie se conoce como "bajar la altura" desde ese vértice. Es un caso especial de proyección.

    Las alturas se pueden usar en el cálculo del área de un triángulo: el semiproducto de la longitud de una altura y la longitud de su base . Por lo tanto, la altura más larga es perpendicular al lado más corto del triángulo, pues cada altura es inversamente proporcional a su respectivo lado. Las alturas también están relacionadas con los lados del triángulo a través de las funciones trigonométricas.

    En un triángulo rectángulo, las alturas de cada ángulo agudo coinciden con un cateto del triángulo, e intersecan el lado opuesto (tienen su pie) en el vértice del ángulo recto, que es el ortocentro.

    En un triángulo isósceles (un triángulo con dos lados congruentes), la altura que tiene el lado incongruente como base tendrá el punto medio de ese lado como su pie. También la altura que tiene el lado incongruente como su base será la bisectriz del ángulo del vértice.

    Es común marcar la altura con la letra , a menudo acompañada con la letra del lado sobre el que se levanta.

    En un triángulo rectángulo, la altura trazada sobre la hipotenusa , divide la hipotenusa en dos segmentos de longitudes y . Si se denomina la longitud de la altura por , entonces se verifica la relación

    {\displaystyle h_{c}={\sqrt {pq}}}

    (Teorema geométrico principal)

    Las alturas de cada uno de los ángulos agudos de un triángulo obtuso se encuentran completamente fuera del triángulo, al igual que el ortocentro H.

    Para triángulos agudos y rectángulos, los pies de las alturas caen todos sobre los lados del triángulo (no extendidos). En un triángulo obtuso, el pie de la altura desde el vértice del ángulo obtuso cae en el interior del lado opuesto, pero los pies de las alturas a los vértices de los ángulos agudos caen en el lado extendido, en el exterior al triángulo Esto se ilustra en el diagrama adyacente: en este triángulo obtuso, una altura trazada perpendicularmente desde el vértice superior, que tiene un ángulo agudo, corta el lado horizontal extendido fuera del triángulo.

    Ortocentro[editar]

    Véase también:

    Las tres alturas (extendidas en algunos casos) se cortan en un solo punto, llamado ortocentro del triángulo, generalmente denotado por H.1​2​ El ortocentro se encuentra dentro del triángulo si y solo si el triángulo es agudo (es decir, no tiene ángulo mayor o igual a un ángulo recto). Si uno de los ángulos es recto, el ortocentro coincide con el vértice de este ángulo.2​

    Sean , , los vértices y también los ángulos de un triángulo, y sean = ||, = ||, = || las longitudes de los lados. El ortocentro tiene coordenadas trilineales3​

    {\displaystyle \sec A:\sec B:\sec C=\cos A-\sin B\sin C:\cos B-\sin C\sin A:\cos C-\sin A\sin B,}

    y coordenadas baricéntricas

    {\displaystyle \displaystyle (a^{2}+b^{2}-c^{2})(a^{2}-b^{2}+c^{2}):(a^{2}+b^{2}-c^{2})(-a^{2}+b^{2}+c^{2}):(a^{2}-b^{2}+c^{2})(-a^{2}+b^{2}+c^{2})}

    {\displaystyle =\tan A:\tan B:\tan C.}

    Como las coordenadas baricéntricas son todas positivas para un punto en el interior de un triángulo, pero al menos una es negativa para un punto en el exterior, y dos de las coordenadas baricéntricas son cero para un punto de vértice, las coordenadas baricéntricas dadas para el ortocentro muestran que el ortocentro está en el interior de un triángulo agudo, en el vértice del ángulo recto de un triángulo rectángulo y en el exterior a un triángulo obtuso.

    Dado el plano complejo, sean los puntos , y C, que representan respectivamente los números complejos

    {\displaystyle z_{A}}

    ,

    {\displaystyle z_{B}}

    y

    {\displaystyle z_{C}}

    y supóngase que el circuncentro del triángulo ABC se encuentra en el origen del plano. Entonces, el número complejo

    {\displaystyle z_{H}=z_{A}+z_{B}+z_{C}}

    está representado por el punto H, es decir, el ortocentro del triángulo ABC.4​ A partir de esto, las siguientes caracterizaciones del ortocentro H mediante vectores libres se pueden establecer de manera directa:

    {\displaystyle {\vec {OH}}=\sum \limits _{\scriptstyle {\rm {cyclic}}}{\vec {OA}},\qquad 2\cdot {\vec {HO}}=\sum \limits _{\scriptstyle {\rm {cyclic}}}{\vec {HA}}.}

    fuente : es.wikipedia.org

    cierto o falso: una altura de un triangulo es un segmento de recta que va de un vertice y es

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    fuente : brainly.lat

    ¿Quieres ver la respuesta o más?
    Santiago 18 day ago
    4

    Chicos, ¿alguien sabe la respuesta?

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