line up - lines up with itself


Senior Member
Spanish, Argentina
Queridos foreros:
En un texto de ejercicios de matemática para primaria en el que hay que completar los espacios en blanco dice lo siguiente:
Call the midpoint of segment CD ___ . Construct the perpendicular bisector of segment CD. The perpendicular bisector of CD must go through B since it's the midpoint. A is also on the perpendicular of CD because the distance from A to ___ is the same as the distance from A to ___ . We want to show triangle ADC is congruent to triangle ACD. Reflect triangle ADC across line ___ . Since ___ is on the line of reflection, it definitely lines up with itself.

Quería pedirles ayuda para comprender lo subrayado.
Como ___ se encuentra en la línea de reflexión, sin dudas "se alinea consigo mismo/a" (no sé qué cabe en el espacio en blanco).

Sus sugerencias son bienvenidas, ¡muchas gracias de antemano!
  • Masood

    Senior Member
    British English
    Just guesswork, based on the image I tried to draw, which is probably wrong. The question is asking us to show that the yellow triangle on the left is the same size as the one on the right (congruency). The term "lines up with itself" is poor and open to interpretation, moreso if there's no accompanying diagram! I think a more accurate description would be "are mirror images of each other".

    Also I think there's a typo in the question, because it says "We want to show triangle ADC is congruent to triangle ACD"...and unless I'm mistaken, this is two ways to refer to the same triangle!
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    Senior Member
    UK English
    I agree there is probably a typo here. The point he has marked as M is actually B, I think. So ABC and ABD are congruent triangles.

    If you reflect ABC across line AB then AB is reflected onto itself, which is what "lines up with itself" means (or is at least intended to mean here) Perhaps "coincide" ??

    Presumably the proof then continues to state that CB is the same length as BD and AC the same length as AD.

    ... QED :)

    And, as Masood says, ACD and ADC are congruent by definition as any triangle has the same line lengths and angles as itself - no proof needed.

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