[ "DEF", "GHI", "Both", "None" ] {DEF:"<code>DEF</code>",GHI:"<code>GHI</code>",Both:$._("Ambos"),None:$._("Ninguno")} ANSWERS[randRange(0, 3)]
randomSides() randRange(1, 3)/2 randRange(1, 3)/2 ANSWER === "DEF" || ANSWER === "Both" ? scaleSides(ABC_SIDES, SCALE_DEF) : randomSides(ABC_SIDES) ANSWER === "GHI" || ANSWER === "Both" ? scaleSides(ABC_SIDES, SCALE_GHI) : randomSides(ABC_SIDES)
triangleAngles( ABC_SIDES ) ANSWER === "DEF" || ANSWER === "Both" ? ABC_ANGLES : triangleAngles(DEF_SIDES) ANSWER === "GHI" || ANSWER === "Both" ? ABC_ANGLES : triangleAngles(GHI_SIDES) "\\neq" ABC_SIDES[2] / DEF_SIDES[2] === ABC_SIDES[0] / DEF_SIDES[0] ? "=" : "\\neq" ABC_SIDES[0] / DEF_SIDES[0] === ABC_SIDES[1] / DEF_SIDES[1] ? "=" : "\\neq" ABC_SIDES[2] / GHI_SIDES[2] === ABC_SIDES[0] / GHI_SIDES[0] ? "=" : "\\neq" ABC_SIDES[0] / GHI_SIDES[0] === ABC_SIDES[1] / GHI_SIDES[1] ? "=" : "\\neq" function(){var e=new Triangle([2,-1],ABC_ANGLES,5,{});return e.labels={sides:[ABC_SIDES[2],ABC_SIDES[0],ABC_SIDES[1]],points:["A","B","C"]},e.rotate(randRange(0,360)),e.boxOut([[[-4,1.5],[10,1.5]]],[0,-.5]),e}() function(){var e=new Triangle([1,-8],DEF_ANGLES,5*SCALE_DEF,{});return e.labels={sides:[DEF_SIDES[2],DEF_SIDES[0],DEF_SIDES[1]],points:["D","E","F"]},e.rotate(randRange(0,360)),e.color="blue",e.boxOut([[[-1,-10],[-1,20]]],[.5,0]),e.boxOut(TR.sides,[0,-1]),e}() function(){var e=new Triangle([8,-6.5],GHI_ANGLES,5*SCALE_GHI,{});return e.labels={sides:[GHI_SIDES[2],GHI_SIDES[0],GHI_SIDES[1]],points:["G","H","I"]},e.rotate(randRange(0,360)),e.color="red",e.boxOut([[[13,-10],[13,20]]],[-.5,0]),e.boxOut(TR.sides,[0,-1]),e.boxOut(TR_A.sides,[0,-1]),e}()
¿Qué triángulos son semejantes al triángulo ABC?
init({range:[[-1,13],[-14,2.5]],scale:35}),TR.draw(),TR.drawLabels(),style({stroke:"blue"}),TR_A.draw(),TR_A.drawLabels(),style({stroke:"red"}),TR_B.draw(),TR_B.drawLabels()
ANSWER_DISPLAY[ ANSWER ]
  • ANS

Los lados de triángulos semejantes siempre son proporcionales. Esto se conoce como

\color{orange}{Side-Side-Side (SSS) Similarity}.

Primero determinemos si ABC y DEF son semejantes.

En el triángulo DEF, DE = DEF_SIDES[2], EF = DEF_SIDES[0], y FD = DEF_SIDES[1].

En el triángulo ABC, AB = ABC_SIDES[2], BC = ABC_SIDES[0], y CA = ABC_SIDES[1].

Para que ABC y DEF sean similares:

\dfrac{AB}{\color{blue}{DE}} = \dfrac{BC}{\color{blue}{EF}} = \dfrac{CA}{\color{blue}{FD}}

Sustituye los valores apropiados para cada lado.

\dfrac{ABC_SIDES[2]}{\color{blue}{DEF_SIDES[2]}} DEF_COMP_1 \dfrac{ABC_SIDES[0]}{\color{blue}{DEF_SIDES[0]}} DEF_COMP_2 \dfrac{ABC_SIDES[1]}{\color{blue}{DEF_SIDES[1]}}

Dado que no todas la proporciones son iguales, ABC no es semejante a DEF.

Como todas las proporciones son iguales, ABC es semejante a DEF.

Ahora, determinemos si ABC y GHI son semejantes.

En el triángulo GHI, GH = GHI_SIDES[2], HI = GHI_SIDES[0] y IG = GHI_SIDES[1].

En el triángulo ABC, AB = ABC_SIDES[2], BC = ABC_SIDES[0], y CA = ABC_SIDES[1].

Para que los triángulos ABC y GHI sean semejantes:

\dfrac{AB}{\color{red}{GH}} = \dfrac{BC}{\color{red}{HI}} = \dfrac{CA}{\color{red}{IG}}

Sustituye los valores apropiados para cada lado.

\dfrac{ABC_SIDES[2]}{\color{red}{GHI_SIDES[2]}} GHI_COMP_1 \dfrac{ABC_SIDES[0]}{\color{red}{GHI_SIDES[0]}} GHI_COMP_2 \dfrac{ABC_SIDES[1]}{\color{red}{GHI_SIDES[1]}}

Dado que no todas las proporciones son iguales, ABC no es semejante a GHI.

Dado que todas las proporciones son iguales, ABC es similar a GHI.

DEF es semejante a ABC

GHI es semejante a ABC

DEF y GHI son semejantes a ABC

Ni DEF ni GHI son semejantes a ABC