new Seg("A","B") AB new Seg("A","C") AC AD new Seg("A","F") AF new Seg("B","C") BC new Seg("B","D") BD new Seg("B","E") BE new Seg("C","E") CE new Seg("C","F") CF new Seg("D","E") DE new Seg("D","F") DF new Seg("E","F") EF [AB,BA,AC,CA,AD,DA,AF,FA,BC,CB,BD,DB,BE,EB,CE,EC,CF,FC,DE,ED,DF,FD,EF,FE] new Ang("B","A","C") new Ang("A","B","C") new Ang("A","C","B") new Ang("D","B","E") new Ang("E","B","C") new Ang("B","C","E") new Ang("E","C","F") new Ang("B","D","E") new Ang("B","E","D") new Ang("B","E","C") new Ang("C","E","F") new Ang("C","F","E") [ang1, ang2, ang3, ang4, ang5, ang6, ang7, ang8, ang9, ang10, ang11, ang12] [addAngs(ang2, addAngs(ang5, ang4)), addAngs(ang3, addAngs(ang6, ang7)), addAngs(ang9, addAngs(ang10,ang11))] [[ang5, ang9], [ang6, ang11]] new Triang([AB, BC, CA], [ang2, ang3, ang1]) new Triang([BD, DE, EB], [ang8, ang9, ang4]) new Triang([BC, CE, EB], [ang6, ang10, ang5]) new Triang([CE, EF, FC], [ang11, ang12, ang7]) new Triang([AD, DF, FA], [ang8, ang12, ang1]) [ABC, BDE, BCE, CEF] initProof(SEGS, ANGS, TRIANGLES, SUPPLEMENTARY_ANGS, ALTERNATE_INTERIOR_ANGS, 3, 0.25, "all") STATEMENTS[0] STATEMENTS[1] KhanUtil.random() < 0.7 IS_WRONG ? outputBadProof() : outputFinishedProof() PROOF_STUFF[0] PROOF_STUFF[1] PROOF_STUFF[2] KhanUtil.random() < 0.5 IS_WRONG ? WRONG_STATEMENT : "There's no wrong statement: this proof is fine."

What's the first wrong statement in the proof below that FINISHED \; ?

\overline{BC} is parallel to \overline{DF} . This diagram is not drawn to scale.

init({ range: [[-5, 5], [-5, 5]], scale: 40 }); addMouseLayer(); graph.congruency = addCongruency({ y1: -0.7, y2: 10.7 }); graph.congruency.addPoint("A", [0, 4]); graph.congruency.addPoint("B", [-2, 0]); graph.congruency.addPoint("C", [2, 0]); graph.congruency.addPoint("D", [-4, -4]); graph.congruency.addPoint("E", [0, -4]); graph.congruency.addPoint("F", [4, -4]); graph.congruency.addLine({ start: "A", end: "B", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "A", end: "C", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "A", end: "D", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "A", end: "F", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "B", end: "C", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "B", end: "D", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "B", end: "E", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "C", end: "E", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "C", end: "F", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "D", end: "E", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "D", end: "F", clickable: true, maxState: 3 }); graph.congruency.addLine({ start: "E", end: "F", clickable: true, maxState: 3 }); graph.congruency.addAngles("A", { maxState: 3 }); graph.congruency.addAngles("B", { maxState: 3 }); graph.congruency.addAngles("C", { maxState: 3 }); graph.congruency.addAngles("D", { maxState: 3 }); graph.congruency.addAngles("E", { maxState: 3 }); graph.congruency.addAngles("F", { maxState: 3 }); graph.congruency.addAngle("BAC", { maxState: 3 }); graph.congruency.addAngle("EDB", { maxState: 3 }); graph.congruency.addAngle("CFE", { maxState: 3 }); for(var angle in graph.congruency.angles){ graph.congruency.angles[angle].setSelectedStyle({ stroke: "black", "stroke-width": 3 }); } graph.congruency.addLabel("A", "above"); graph.congruency.addLabel("B", "left"); graph.congruency.addLabel("C", "right"); graph.congruency.addLabel("D", "below"); graph.congruency.addLabel("E", "below"); graph.congruency.addLabel("F", "below"); for(var angle in graph.congruency.angles){ graph.congruency.angles[angle].setSelectedStyle({ stroke: "black", "stroke-width": 3 }); } for(var line in graph.congruency.lines){ for(var line2 in graph.congruency.lines){ (function(){ var $statement = $("."+line+"-"+line2); var firstLine = graph.congruency.lines[line]; var secondLine = graph.congruency.lines[line2]; if($statement.length > 0){ $statement.live("vmouseover", function(event) { firstLine.setHighlighted({ stroke: ORANGE, "stroke-width": 3 }); secondLine.setHighlighted({ stroke: BLUE, "stroke-width": 3 }); $(this).bind("vmouseout", function(event) { firstLine.unsetHighlighted(); secondLine.unsetHighlighted(); }); }); } })(); } } for(var angle in graph.congruency.angles){ for(var angle2 in graph.congruency.angles){ (function(){ var $statement = $("."+angle+"-"+angle2); var firstAngle = graph.congruency.angles[angle]; var secondAngle = graph.congruency.angles[angle2]; if($statement.length > 0){ $statement.live("vmouseover", function(event) { var firstState = firstAngle.state; var secondState = secondAngle.state; var maxState = Math.max(firstState,secondState); firstAngle.setHighlighted({ stroke: ORANGE, "stroke-width": 3 }); secondAngle.setHighlighted({ stroke: BLUE, "stroke-width": 3 }); firstAngle.setState(maxState > 0 ? maxState : 1); secondAngle.setState(maxState > 0 ? maxState : 1); $(this).bind("vmouseout", function(event) { firstAngle.unsetHighlighted(); secondAngle.unsetHighlighted(); firstAngle.setState(firstState); secondAngle.setState(secondState); }); }); } })(); } } for(var line in graph.congruency.lines){ (function(){ var $statements = $("."+line); for(var i = 0; i<$statements.length; i++){ var highlightLine = graph.congruency.lines[line]; var highlightDiv = $($statements[i]); highlightDiv.live("vmouseover", function(event) { highlightLine.setHighlighted({ stroke: ORANGE, "stroke-width": 3 }); $(this).bind("vmouseout", function(event) { highlightLine.unsetHighlighted({ stroke: "black", "stroke-width": 2 }); }); }); } })(); } for(var line in graph.congruency.lines){ (function(){ var $statements = $("."+line + "2"); for(var i = 0; i<$statements.length; i++){ var highlightLine = graph.congruency.lines[line]; var highlightDiv = $($statements[i]); highlightDiv.live("vmouseover", function(event) { highlightLine.setHighlighted({ stroke: BLUE, "stroke-width": 3 }); $(this).bind("vmouseout", function(event) { highlightLine.unsetHighlighted({ stroke: "black", "stroke-width": 2 }); }); }); } })(); }

PROOF

ANSWER
  • WRONG_STATEMENT
  • RIGHT_STATEMENT
  • There's no wrong statement: this proof is fine.
  • RIGHT_STATEMENT
  • WRONG_STATEMENT
  • There's no wrong statement: this proof is fine.

Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof.

WRONG_STATEMENT is the first wrong statement.

There is no wrong statement in this proof.