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6-96.

Para cada uno de los siguientes puntos, decide si los triángulos son semejantes. Si son semejantes, utiliza su semejanza para resolver para x. Si no son semejantes, explica por qué.  

  1. A triangle with an internal horizontal line drawn parallel to the base forming an internal triangle sharing the top vertex. For the internal triangle, the left side is 8 and the right side is 13. For the main triangle the left side is 8 + 5 and the right side s 13 + x.

    Los triángulos comparten un ángulo común y las rectas paralelas tienen ángulos correspondientes congruentes, por tanto, los triángulos son semejantes por .

  1. A transversal segment connects the ends of two parallel line segments, 5, and x. A triangle is formed when the opposite end of the parallel segment, 5, has a diagonal line segment, 8, that connects at the point where the transversal connects to the parallel segment, x. And at the end of the parallel segment, x, another diagonal line, 4, connects to a point further along on the transversal forming a second triangle.

    ¿Hay suficiente información para probar que los triángulos son semejantes?

  1. Two parallel line segments, length, x, and 8, have at each end, lines crisscrossing to the opposite end of the other parallel line segment forming two triangles when the lines intersect. one triangle has sides, x, 8, and unknown. The other triangle has sides 6, 8, and 4. Two of the sides, 8, and 6 are on the same line between the two triangles.

    In the triangle with sides x, and 8, angle theta is opposite side 8 and angle alpha is opposite side, x. In the triangle with sides 6, 8, and 4, angle beta is opposite side 8 and angle gamma is opposite side 6. Angles alpha and beta are vertical angles.

    Los ángulos opuestos por el vértice son congruentes, entonces, .
    Las rectas paralelas tienen ángulos alternos internos iguales, entonces .
    Los triángulos son semejantes por .