"abcdefghijklmnpqrstuvwxyz" randRange( 0, LETTERS.length - 1 ) LETTERS[ LETTER ] randRangeUnique(0, 4, 2) pickLabels(POINT_LABELS)
randRange(1, 5)/2 randRange(1, 5)/2
randomSides() scaleSides(BASE_SIDES, SCALE_A) triangleAngles(A_SIDES) scaleSides(BASE_SIDES, SCALE_B) triangleAngles(B_SIDES) randRange(0, 2) SOLUTION_INDEX === 2 ? 0 : SOLUTION_INDEX + 1 SOLUTION_INDEX === 0 ? 2 : SOLUTION_INDEX - 1 B_SIDES[SOLUTION_INDEX] insertVariable(SOLUTION_INDEX, X, B_SIDES) fractionReduce(B_SIDES[PROP_INDEX], A_SIDES[PROP_INDEX]) function(){var e=new Triangle([0,-2],A_ANGLES,5*SCALE_A,{});return e.labels={sides:[A_SIDES[2],A_SIDES[0],A_SIDES[1]],points:A_POINTS},e.rotate(randRange(0,360)),e.color=BLUE,e}() function(){var e=new Triangle([8,-6],B_ANGLES,5*SCALE_B,{});return e.labels={sides:[B_LABELS[2],B_LABELS[0],B_LABELS[1]],points:B_POINTS},e.rotate(randRange(0,360)),e.color=RED,e.boxOut(TR_A.sides,[0,-1]),e}()

El triángulo A_NAME es semejante al triángulo B_NAME.

Resuelve para X.

TR_A.rotate(randRange(0,360)),TR_B.rotate(randRange(0,360));var aBounding=TR_A.boundingRange(1),bBounding=TR_B.boundingRange(1),minX=Math.min(aBounding[0][0],bBounding[0][0]),maxX=Math.max(aBounding[0][1],bBounding[0][1]),minY=Math.min(aBounding[1][0],bBounding[1][0]),maxY=Math.max(aBounding[1][1],bBounding[1][1]);init({range:[[minX,maxX],[minY,maxY]],scale:500/(maxX-minX)}),style({stroke:BLUE}),TR_A.draw(),TR_A.drawLabels(),style({stroke:RED}),TR_B.draw(),TR_B.drawLabels()
SOLUTION

X = \quad

Los triángulos semejantes tiene lados proporcionales.

Por lo tanto, podemos establecer proporciones equivalente y resolver para X.

\dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\blue{A_SIDES[SOLUTION_INDEX]}} = \dfrac{\red{B_LABELS[PROP_INDEX]}}{\blue{A_SIDES[PROP_INDEX]}}

Note: As each corresponding \dfrac{\red{side}}{\blue{side}} proportion is equivalent, you could use the other sides (i.e., \dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\blue{A_SIDES[SOLUTION_INDEX]}} = \dfrac{\red{B_LABELS[ALTERNATE_INDEX]}}{\blue{A_SIDES[ALTERNATE_INDEX]}})

Reduce la proporción en el lado derecho.

\dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\blue{A_SIDES[SOLUTION_INDEX]}} = \cancel{\dfrac{\red{B_LABELS[PROP_INDEX]}}{\blue{A_SIDES[PROP_INDEX]}}}{\green{fractionReduce(B_LABELS[PROP_INDEX], A_SIDES[PROP_INDEX])}}

Multiplica cada lado por A_SIDES[SOLUTION_INDEX] y simplifica.

\cancel{A_SIDES[SOLUTION_INDEX]} \times \dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\cancel{\blue{A_SIDES[SOLUTION_INDEX]}}} = \green{fractionReduce(B_LABELS[PROP_INDEX], A_SIDES[PROP_INDEX])} \times A_SIDES[SOLUTION_INDEX]

\red{X} es igual a SOLUTION.