randRangeUnique( 0, 3, 2 )
randFromArray( ANG_FIRST )
ANG_FIRST
clearArray( [ "x", "x", "x" ], [ ANG_LEFT ] )
TR_B.angles[ ANG_LEFT ]
These two triangles have three sides equal (they share one of them).
Therefore they are congruent.
Congruent triangles also have congruent (equal) angles.
If we superimpose these two triangles, by rotating triangle ABC, we see that angle x corresponds to angle ANGLE_LABELS[ ANG_LEFT ]
Angle x is therefore equal to ANSWER.
randRangeUnique( 0, 3, 2 )
randRangeExclude( 0, 2, ANG_FIRST )
ANG_FIRST
clearArray( [ "x", "x", "x" ], [ ANG_LEFT ] )
TR_B.angles[ ANG_LEFT ]
These two triangles have three sides equal (they share one of them).
Therefore they are congruent.
Congruent triangles also have congruent (equal) angles.
If we superimpose these two triangles, by rotating triangle ABC, we see that angle x corresponds to angle ANGLE_LABELS[ ANG_LEFT ].
ANGLE_LABELS[ ANG_LEFT ] = 180 - TR_A.angles[ ANG_FIRST[ 0 ] ] - TR_A.angles[ ANG_FIRST[ 1 ] ]
ANGLE_LABELS[ ANG_LEFT ] = x = TR_B.angles[ ANG_LEFT ]
TR_A.labels.angles = TR_A.niceAngles;
TR_A.drawLabels();
function(){
var newAng = RAND_ANG;
if ( RAND_ANG == 0 ){
newAng = 1;
}
else if ( RAND_ANG == 1 ){
newAng = 0;
}
return newAng;
}()
[ 0, 1 ]
randRangeUnique( 0, 3, 2 )
randRange( 0, 2 )
function(){
if ( ANG_LEFT == 1 ){
return 0;
}
if ( ANG_LEFT == 0 ){
return 1;
}
return 2;
}()
( jQuery.inArray( SHOW_ANGLE, ANG_FIRST ) !== -1 )
ANG_FIRST
clearArray( [ "x", "x", "x" ], [ ANG_LEFT ] )
ANGLES[ 0 ] / 2
function(){
var trA = new Triangle( [ 7, -3 ], ANGLES ,6, {} );
trA.rotationCenter = trA.points[ 0 ];
trA.rotate( ANG );
trA.labels = { "points" : [ "", "B", "C" ], "sides" : clearArray( trA.niceSideLengths, SIDES_A ), "angles" : clearArray( trA.niceAngles, ANGLES_A ) };
return trA;
}()
function(){
var trB = new Triangle( [ 7 - cos( ANG * PI / 180 ) * TR_A.sideLengths[ 0 ], -3 - sin( ANG * PI / 180 ) * TR_A.sideLengths[ 0 ] ], [ ANGLES[ 1 ], ANGLES[ 0 ], ANGLES[ 2 ] ] , 6, {} );
trB.rotationCenter = trB.points[ 0 ];
trB.rotate( -ANG );
trB.labels = { "points" : [ "D", "", "E" ], "sides" : clearArray( trB.niceSideLengths, SIDES_B ), "angles" : ANGLES_B };
return trB;
}()
TR_B.angles[ ANG_LEFT ]
init({
range: [ [-1, 15 ], [ -7, 2.5 ] ]
})
TR_A.draw();
TR_A.drawLabels();
TR_B.draw();
TR_B.drawLabels();
label( TR_B.points[ 1 ], "A", "above" );
ANSWER
These two triangles have two sides and an angle equal.
Therefore they are congruent.
Congruent triangles also have congruent (equal) angles.
If we superimpose these two triangles, by flipping triangle EDA
, we see that angle x corresponds to angle ANGLE_LABELS[ SHOW_ANGLE ]
ANGLE_LABELS[ SHOW_ANGLE ] = 180 - TR_A.angles[ ANG_FIRST[ 0 ] ] - TR_A.angles[ ANG_FIRST[ 1 ] ]
ANGLE_LABELS[ SHOW_ANGLE ] = x = TR_B.angles[ ANG_LEFT ]
TR_A.labels.angles = TR_A.niceAngles;
TR_A.drawLabels();
Angle x is therefore equal to ANSWER