randomTriangle()
[
["B", "B"],
["C", "C"],
["Both", $._("Both")],
["None", $._("None")]
]
randFromArray( ANSWERS )
ANSWER === "B" || ANSWER === "Both" ? shuffle( MAIN ) : randomTriangle( MAIN )
ANSWER === "C" || ANSWER === "Both" ? shuffle( MAIN ): randomTriangle( MAIN )
function(){
var tr = new Triangle( [ 3, -2 ], MAIN, 5, {} );
tr.labels = { "name" : "A", "angles" : clearArray( tr.niceAngles, [ 0, 2 ] ) };
tr.rotate( randRange( 0, 360 ) );
tr.boxOut( [ [ [ -4, 1.5 ], [ 10, 1.5 ] ] ], [ 0, -0.5 ] );
return tr;
}()
function(){
var trA = new Triangle( [ 2, -8 ], B, randRange( 400, 600 )/100, { } );
trA.labels = { "name" : "B", "angles" : clearArray( trA.niceAngles, [ 0, 1 ] ) };
trA.rotate( randRange( 0, 360 ) );
trA.color = "blue";
trA.boxOut( [ [ [ -1, -10 ], [ -1, 20 ] ] ], [ 0.5, 0 ] );
trA.boxOut( TR.sides, [ 0, -1 ] );
return trA;
}()
function(){
var trB = new Triangle( [ 7, -6 ], C, randRange( 400, 600 )/100, {} );
trB.labels = { "name" : "C", "angles" : clearArray( trB.niceAngles, [ 0, 2 ] ) };
trB.rotate( randRange( 0, 360 ) );
trB.color = "red";
trB.boxOut( [ [ [ 13, -10 ], [ 13, 20 ] ] ], [ -0.5, 0 ] );
trB.boxOut( TR.sides, [ 0, -1 ] );
trB.boxOut( TR_A.sides, [ 0, -1 ] );
return trB;
}()
Which triangles are similar to triangle A?
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_SHOW
Two triangles are similar if their angles are congruent (equal).
We see that triangle A has angles of MAIN[ 0 ] and MAIN[ 2 ]. The third angle is therefore 180 - MAIN[ 0 ] - MAIN[ 2 ] = MAIN[ 1 ]
TR.labels.angles = TR.niceAngles;
TR.drawLabels();
Triangle B has angles of B[ 0 ] and B[ 1 ]. The third angle is 180 - B[ 0 ] - B[ 1 ] = B[ 2 ].
Therefore triangle B is not similar to triangle A.
Therefore triangle B is similar to triangle A.
style({
stroke: "blue",
});
TR_A.labels.angles = TR_A.niceAngles;
TR_A.drawLabels();
Triangle C has angles of C[ 0 ] and C[ 2 ]. The third angle is 180 - C[ 0 ] - C[ 2 ] = C[ 1 ].
Therefore triangle C is not similar to triangle A.
Therefore triangle C is similar to triangle A.
style({
stroke: "red",
});
TR_B.labels.angles = TR_B.niceAngles;
TR_B.drawLabels();