# Khan/khan-exercises

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 3cd602a Add exercise: Solving Similar Triangles 1 mwahl authored Feb 14, 2012 1 cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 2 3 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 4 113bddd Update the title tags to match real display names spicyj authored Apr 11, 2013 5 Solving similar triangles 1 ac1415e Use requirejs for module loading spicyj authored Mar 5, 2014 6 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 7 3cd602a Add exercise: Solving Similar Triangles 1 mwahl authored Feb 14, 2012 53 54 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 55
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eab6171 Ensure side not given the same letter as a vertex petercollingridge authored Jun 5, 2014 57
58 randVar() 59 pickLabels() 60
61 A_POINTS.join("") 62 B_POINTS.join("") 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 63 64 65 randRange(1, 5)/2 66 randRange(1, 5)/2 67 68 69 randomSides() 70 71 scaleSides(BASE_SIDES, SCALE_A) 72 triangleAngles(A_SIDES) 73 scaleSides(BASE_SIDES, SCALE_B) 74 triangleAngles(B_SIDES) 75 76 randRange(0, 2) 77 SOLUTION_INDEX === 2 ? 0 : SOLUTION_INDEX + 1 78 SOLUTION_INDEX === 0 ? 2 : SOLUTION_INDEX - 1 79 B_SIDES[SOLUTION_INDEX] 80 insertVariable(SOLUTION_INDEX, X, B_SIDES) 81 82 fractionReduce(B_SIDES[PROP_INDEX], A_SIDES[PROP_INDEX]) 83 84 85 function(){ 86 var trA = new Triangle( [ 0, -2 ], A_ANGLES, 5*SCALE_A, {} ); 87 trA.labels = {"sides": [A_SIDES[2], A_SIDES[0], A_SIDES[1]], "points" : A_POINTS }; 88 trA.rotate( randRange( 0, 360 ) ); ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 89 trA.color = BLUE; 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 90 // trA.boxOut( [ [ [ -1, -10 ], [ -1, 20 ] ] ], [ 0.5, 0 ] ); 91 // trA.boxOut( TR.sides, [ 0, -1 ] ); 92 return trA; 93 }() 94 95 96 function(){ 97 var trB = new Triangle( [ 8, -6 ], B_ANGLES, 5*SCALE_B, {} ); 98 trB.labels = {"sides": [B_LABELS[2], B_LABELS[0], B_LABELS[1]], "points" : B_POINTS }; 99 trB.rotate( randRange( 0, 360 ) ); ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 100 trB.color = RED; 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 101 // trB.boxOut( [ [ [ 13, -10 ], [ 13, 20 ] ] ], [ -0.5, 0 ] ); 102 // trB.boxOut( TR.sides, [ 0, -1 ] ); 103 trB.boxOut( TR_A.sides, [ 0, -1 ] ); 104 return trB; 105 }() 106 107 108 109 110 111 112 Triangle A_NAME is similar to triangle B_NAME. 113 233a0b9 Rearrange answer area content within some exercises beneater authored Nov 13, 2014 114 Solve for X. 115 116 d53a57c Two doctypes were being output. Only output one. jeresig authored Apr 16, 2013 117 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 118 TR_A.rotate( randRange( 0, 360 ) ); 119 TR_B.rotate( randRange( 0, 360 ) ); 120 121 var aBounding = TR_A.boundingRange(1); 122 var bBounding = TR_B.boundingRange(1); 123 124 var minX = Math.min(aBounding[0][0], bBounding[0][0]); 125 var maxX = Math.max(aBounding[0][1], bBounding[0][1]); 126 127 var minY = Math.min(aBounding[1][0], bBounding[1][0]); 128 var maxY = Math.max(aBounding[1][1], bBounding[1][1]); 129 130 init({ 064281e Fix up exercises that are too wide for tutorials beneater authored Sep 19, 2012 131 range: [ [minX, maxX ], [ minY, maxY ] ], 132 scale: 500 / (maxX - minX) 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 133 }) 134 135 style({ ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 136 stroke: BLUE, 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 137 }); 138 TR_A.draw(); 139 TR_A.drawLabels(); 140 141 style({ ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 142 stroke: RED, 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 143 }); 144 TR_B.draw(); 145 TR_B.drawLabels(); 146 147 148 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 149 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 150
SOLUTION
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eab6171 Ensure side not given the same letter as a vertex petercollingridge authored Jun 5, 2014 152

X =

4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 153 154 155 156 157 Similar triangles have proportional sides. 158 Therefore, we can set up equivalent proportions and solve for X. 159 ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 160 \dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\blue{A_SIDES[SOLUTION_INDEX]}} = \dfrac{\red{B_LABELS[PROP_INDEX]}}{\blue{A_SIDES[PROP_INDEX]}} 161 Note: As each corresponding \dfrac{\red{side}}{\blue{side}} proportion is equivalent, you could use the other sides (i.e., \dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\blue{A_SIDES[SOLUTION_INDEX]}} = \dfrac{\red{B_LABELS[ALTERNATE_INDEX]}}{\blue{A_SIDES[ALTERNATE_INDEX]}}) 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 162
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Reduce the proportion on the right hand side.

ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 166

\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])}}

4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 167 168 169 170 Multiply each side by A_SIDES[SOLUTION_INDEX] and simplify. ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 171 \cancel{A_SIDES[SOLUTION_INDEX]} \times \dfrac{\red{B_LABELS[SOLUTION_INDEX]}}{\cancel{\blue{A_SIDES[SOLUTION_INDEX]}}} = \green{fractionReduce(B_LABELS[PROP_INDEX], A_SIDES[PROP_INDEX])} \times A_SIDES[SOLUTION_INDEX] 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 172
173 ff00e10 Use modern blue/red colors spicyj authored Nov 17, 2013 174

\red{X} is equal to SOLUTION.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 175 176
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cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 180 181
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