randomTriangleAngles.triangle() [ [ 0, 1 ], [] ] [ [ 1 ], [ 2] ] function(){ var trA = new Triangle( [ 5, -8 ], ANGLES , 14 , {} ); trA.boxOut( [ [ [ 0, -10 ], [ 0, 10 ] ] ], [ 0.4 , 0 ] ); trA.boxOut( [ [ [ 11 , -10 ], [ 11, 10 ] ] ], [ -0.4 , 0 ] ); return trA; }() function(){ var pointD = findIntersection( bisectAngle( TR_A.sides[ 0 ], reverseLine( TR_A.sides[ 2 ] ), 1 ), TR_A.sides[ 1 ] ); return pointD; }() function(){ var trB = new Triangle( [0,0],[], 3, {}, [ TR_A.points[ 0 ], TR_A.points[ 1 ], POINT_D ] ); trB.labels = { "angles" : ["{\\theta}^{\\circ}"], "sides" : mergeArray( clearArray( trB.niceSideLengths, SIDES_B[ 0 ] ), clearArray( [ "?", "?", "?" ], SIDES_B[ 1 ] ) ), "points": [ "A", "B", "D" ] }; return trB; }() function(){ var trC = new Triangle( [0,0],[], 3, {}, [ TR_A.points[ 0 ], POINT_D, TR_A.points[ 2 ] ] ); trC.labels = { "angles" : ["{\\theta}^{\\circ}"] , "sides" : mergeArray( clearArray( trC.niceSideLengths, SIDES_C[ 0 ] ), clearArray( [ "?", "?", "?" ], SIDES_C[ 1 ] ) ), "points": [ "", "", "C" ] }; return trC; }() TR_B.niceSideLengths[ 1 ] TR_B.niceSideLengths[ 0 ] TR_C.niceSideLengths[ 1 ] TR_C.niceSideLengths[ 2 ] TR_B.niceSideLengths[ 1 ] TR_B.niceSideLengths[ 0 ] TR_C.niceSideLengths[ 1 ] TR_C.niceSideLengths[ 2 ]
What is the length of `\overline{AC}`?
init({ range: TR_A.boundingRange(1.5) }) TR_B.draw(); TR_B.drawLabels(); TR_C.draw(); TR_C.drawLabels();

`\angle DAB` and `\angle DAC` are congruent.

Therefore `AD` is the bisector of `\angle CAB`

Angle Bisector Theorem states that `\dfrac{AB}{BD} = \dfrac{AC}{CD}`

roundTo( 1, TEMP_AB * TEMP_CD / TEMP_BD )

What is the length of `\overline{AC}`?

Round to one decimal place.
AC

`\dfrac{AB}{BD} = \dfrac{AC}{CD}`

`AC = \dfrac{AB \times CD}{BD}`

`AC = AC`

roundTo( 1, TEMP_AC * TEMP_BD / TEMP_CD ) [ [ 1 ], [0] ] [ [ 1,2 ], [ ] ]

What is the length of `\overline{AB}`?

Round to one decimal place.
AB

`\dfrac{AB}{BD} = \dfrac{AC}{CD}`

`AB = \dfrac{AC \times BD}{CD}`

`AB = AB`

roundTo( 1, TEMP_AC * TEMP_BD / TEMP_AB ) [ [ 1, 0 ], [] ] [ [ 2 ], [1 ] ]

What is the length of `\overline{CD}`?

Round to one decimal place.
CD

`\dfrac{AB}{BD} = \dfrac{AC}{CD}`

`CD = \dfrac{AC \times BD}{AB}`

`CD = CD`

roundTo( 1, TEMP_AB * TEMP_CD / TEMP_AC ) [ [ 0 ], [ 1 ] ] [ [ 1, 2 ], [ ] ]

What is the length of `\overline{BD}`?

Round to one decimal place.
BD

`\dfrac{AB}{BD } = \dfrac{AC}{CD}`

`BD = \dfrac{AB \times CD}{AC}`

`BD = BD`