# Khan/khan-exercises

Split measuring_segments into 4 exercises

1 parent 4af09e4 commit d1032857476fa60f54a472c9f6d9307fada5991f beneater committed Apr 3, 2012
 @@ -1,318 +0,0 @@ - - - - - Measuring segments - - - - - -
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- sortNumbers( randRangeUnique( -5, 5, 4 ) ) - [ BLUE, GREEN, PINK, ORANGE ] - randRangeUnique( 0, 4, 2 ) - [ "A", "B", "C", "D" ][ IDX_1 ] - [ "A", "B", "C", "D" ][ IDX_2 ] - POINT_1 + POINT_2 - abs( POINTS[ IDX_1 ] - POINTS[ IDX_2 ] ) -
-

What is SEGMENT?

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-
- init({ - range: [ [ -6, 6 ], [ -1, 1 ] ] - }); - style({ stroke: "#999" }); - line( [ -5, 0 ], [ 5, 0 ] ); - for ( var x = -5; x <= 5; x++ ) { - line( [ x, -0.2 ], [ x, 0.2 ] ); - label( [ x, -0.53 ], String( x ).replace( /-(\d)/g, "\\llap{-}$1" ), "center", { color: "#999" } ); - } - style({ strokeWidth: 3.5 }); - line( [ 0, -0.2], [0, 0.2]); - - style({ stroke: COLORS[ 0 ], fill: COLORS[ 0 ] }); - circle( [ POINTS[ 0 ], 0 ], 0.10 ); - style({ stroke: COLORS[ 1 ], fill: COLORS[ 1 ] }); - circle( [ POINTS[ 1 ], 0 ], 0.10 ); - style({ stroke: COLORS[ 2 ], fill: COLORS[ 2 ] }); - circle( [ POINTS[ 2 ], 0 ], 0.10 ); - style({ stroke: COLORS[ 3 ], fill: COLORS[ 3 ] }); - circle( [ POINTS[ 3 ], 0 ], 0.10 ); - label( [ POINTS[ 0 ], 0 ], "A", "above", { color: COLORS[ 0 ] } ); - label( [ POINTS[ 1 ], 0 ], "B", "above", { color: COLORS[ 1 ] } ); - label( [ POINTS[ 2 ], 0 ], "C", "above", { color: COLORS[ 2 ] } ); - label( [ POINTS[ 3 ], 0 ], "D", "above", { color: COLORS[ 3 ] } ); - - - SOLUTION - - - - SEGMENT means the distance from \color{COLORS[ IDX_1 ]}{POINT_1} to - \color{COLORS[ IDX_2 ]}{POINT_2}. - - SEGMENT = |\color{COLORS[ IDX_1 ]}{POINTS[ IDX_1 ]} - \color{COLORS[ IDX_2 ]}{POINTS[ IDX_2 ]}| - SEGMENT = |POINTS[ IDX_1 ] - POINTS[ IDX_2 ]| - SEGMENT = SOLUTION - - - - - - randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ]) - POINTS[ 0 ] + POINTS[ 1 ] - POINTS[ 1 ] + POINTS[ 2 ] - POINTS[ 0 ] + POINTS[ 2 ] - randRangeNonZero( 2, 9 ) - randRangeNonZero( 2, 9 ) - randRangeNonZero( 2, 9 ) - randRangeNonZero( 2, 9 ) - randRange( 1, 9 ) - ( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 ) - shuffle([ - [ BLUE, SEG_1 + " = " + COEF_1 + "x + " + CONST_1 ], - [ GREEN, SEG_2 + " = " + COEF_2 + "x + " + CONST_2 ], - [ "purple", SEG_TOTAL + " = " + TOTAL ] - ]) - - - - init({ - range: [ [ -1, 11 ], [ -1, 1 ] ] - }); - line( [ 0, 0 ], [ 10, 0 ] ); - style({ stroke: "#000", fill: "#000" }); - graph.points = raphael.set(); - graph.points.push( circle( [ 0, 0 ], 0.10 ) ); - graph.points.push( circle( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], 0.10 ) ); - graph.points.push( circle( [ 10, 0 ], 0.10 ) ); - label( [ 0, 0 ], POINTS[ 0 ], "below" ); - label( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], POINTS[ 1 ], "below" ); - label( [ 10, 0 ], POINTS[ 2 ], "below" ); - - - If: - \qquad GIVEN[ 0 ][ 1 ], - \qquad GIVEN[ 1 ][ 1 ], and - \qquad GIVEN[ 2 ][ 1 ], - - - Find SEG_2. - COEF_2 * X + CONST_2 - - - - style({ stroke: BLUE, strokeWidth: 3 }); - line( [ 0, 0 ], [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ] ); - style({ stroke: GREEN, strokeWidth: 3 }); - line( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], [ 10, 0 ] ); - graph.points.toFront(); - jQuery( "#given0" ).css({ "color": GIVEN[ 0 ][ 0 ] }); - jQuery( "#given1" ).css({ "color": GIVEN[ 1 ][ 0 ] }); - jQuery( "#given2" ).css({ "color": GIVEN[ 2 ][ 0 ] }); - - From the diagram, we can see that the total length of \purple{SEG_TOTAL} is the sum of \blue{SEG_1} and \green{SEG_2}: - \qquad \blue{SEG_1} + \green{SEG_2} = \purple{SEG_TOTAL} - - - Substitute in the expressions that were given for each length: - \qquad \blue{COEF_1x + CONST_1} + \green{COEF_2x + CONST_2} = \purple{TOTAL} - - - Combine like terms: - \qquadCOEF_1 + COEF_2x + CONST_1 + CONST_2 = \purple{TOTAL} - - - Subtract CONST_1 + CONST_2 from both sides: - \qquadCOEF_1 + COEF_2x = TOTAL - CONST_1 - CONST_2 - - - Divide both sides by COEF_1 + COEF_2 to find x: - \qquad x = X - - - Substitute X for x in the expression that was given for SEG_2: - \qquad SEG_2 = COEF_2(\pink{X}) + CONST_2 - - - Simplify: - \qquad \green{SEG_2 = COEF_2 * X + CONST_2} - - - Simplify to find \green{SEG_2}: - \qquad \green{SEG_2 = COEF_2 * X + CONST_2} - - - - - - - random() < 0.5 ? "Yes" : "No" - - sortNumbers( randRangeUnique( -5, 5, 4 ) ) - - [ BLUE, GREEN, PINK, ORANGE ] - - Are \overline{AB} and \overline{CD} congruent? - - - init({ - range: [ [ -6, 6 ], [ -1, 1 ] ] - }); - style({ stroke: "#999" }); - line( [ -5, 0 ], [ 5, 0 ] ); - for ( var x = -5; x <= 5; x++ ) { - line( [ x, -0.2 ], [ x, 0.2 ] ); - label( [ x, -0.53 ], String( x ).replace( /-(\d)/g, "\\llap{-}$1" ), "center", { color: "#999" } ); - } - style({ strokeWidth: 3.5 }); - line( [ 0, -0.2], [0, 0.2]); - - style({ stroke: COLORS[ 0 ], fill: COLORS[ 0 ] }); - circle( [ POINTS[ 0 ], 0 ], 0.10 ); - style({ stroke: COLORS[ 1 ], fill: COLORS[ 1 ] }); - circle( [ POINTS[ 1 ], 0 ], 0.10 ); - style({ stroke: COLORS[ 2 ], fill: COLORS[ 2 ] }); - circle( [ POINTS[ 2 ], 0 ], 0.10 ); - style({ stroke: COLORS[ 3 ], fill: COLORS[ 3 ] }); - circle( [ POINTS[ 3 ], 0 ], 0.10 ); - label( [ POINTS[ 0 ], 0 ], "A", "above", { color: COLORS[ 0 ] } ); - label( [ POINTS[ 1 ], 0 ], "B", "above", { color: COLORS[ 1 ] } ); - label( [ POINTS[ 2 ], 0 ], "C", "above", { color: COLORS[ 2 ] } ); - label( [ POINTS[ 3 ], 0 ], "D", "above", { color: COLORS[ 3 ] } ); -
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SOLUTION
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• Yes
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• No
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Congruent segments have equal lengths.

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Find the lengths of \overline{AB} and \overline{CD}:

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- AB = |\color{COLORS[ 0 ]}{POINTS[ 0 ]} - \color{COLORS[ 1 ]}{POINTS[ 1 ]}| - CD = |\color{COLORS[ 2 ]}{POINTS[ 2 ]} - \color{COLORS[ 3 ]}{POINTS[ 3 ]}| -

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- AB = |POINTS[ 0 ] - POINTS[ 1 ]| - CD = |POINTS[ 2 ] - POINTS[ 3 ]| -

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- AB = POINTS[ 1 ] - POINTS[ 0 ] - CD = POINTS[ 3 ] - POINTS[ 2 ] -

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AB = CD

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Yes, \overline{AB} and \overline{CD} are congruent.

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AB \neq CD

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No, \overline{AB} and \overline{CD} are not congruent.

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- randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ]) - POINTS[ 0 ] + POINTS[ 1 ] - POINTS[ 1 ] + POINTS[ 2 ] - POINTS[ 0 ] + POINTS[ 2 ] -
- randRange( 1, 9 ) - randRangeNonZero( 2, 9 ) - randRangeNonZero( -9, 9 ) - randRangeNonZero( 2, 9 ) - COEF_1 * X + CONST_1 - COEF_2 * X - ( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 ) -
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POINTS[ 1 ] is the midpoint of \overline{SEG_TOTAL}

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- init({ - range: [ [ -1, 11 ], [ -1, 1 ] ] - }); - line( [ 0, 0 ], [ 10, 0 ] ); - style({ stroke: "#000", fill: "#000" }); - graph.points = raphael.set(); - graph.points.push( circle( [ 0, 0 ], 0.10 ) ); - graph.points.push( circle( [ 5, 0 ], 0.10 ) ); - graph.points.push( circle( [ 10, 0 ], 0.10 ) ); - label( [ 0, 0 ], POINTS[ 0 ], "below" ); - label( [ 5, 0 ], POINTS[ 1 ], "below" ); - label( [ 10, 0 ], POINTS[ 2 ], "below" ); -
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- If:
- \qquad SEG_1 = COEF_1x + CONST_1 and
- \qquad SEG_2 = COEF_2x + CONST_2
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Find SEG_TOTAL.

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TOTAL
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A midpoint divides a segment into two segments with equal lengths.

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- style({ stroke: BLUE, strokeWidth: 3 }); - line( [ 0, 0 ], [ 5, 0 ] ); - style({ stroke: GREEN, strokeWidth: 3 }); - line( [ 5, 0 ], [ 10, 0 ] ); - graph.points.toFront(); - jQuery( "#given1" ).css({ "color": BLUE }); - jQuery( "#given2" ).css({ "color": GREEN }); -
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\blue{SEG_1} = \green{SEG_2}

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Substitute in the expressions that were given for each length:

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\qquad \blue{COEF_1x + CONST_1} = \green{COEF_2x + CONST_2}

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Solve for x:

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\qquad expr([ "*", COEF_1 - COEF_2, "x" ]) = CONST_2 - CONST_1

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- Substitute X for x in the expressions that were given for - SEG_1 and SEG_2: -

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- \qquad SEG_1 = COEF_1(\pink{X}) + CONST_1 - \qquad SEG_2 = COEF_2(\pink{X}) + CONST_2 -

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- \qquad SEG_1 = COEF_1 * X + CONST_1 - \qquad SEG_2 = COEF_2 * X + CONST_2 -

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- \qquad SEG_1 = COEF_1 * X + CONST_1 - \qquad SEG_2 = COEF_2 * X + CONST_2 -

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To find the length SEG_TOTAL, add the lengths \blue{SEG_1} and \green{SEG_2}:

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\qquad SEG_TOTAL = \blue{SEG_1} + \green{SEG_2}

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\qquad SEG_TOTAL = \blue{COEF_1 * X + CONST_1} + \green{COEF_2 * X + CONST_2}

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 @@ -0,0 +1,65 @@ + + + + + Measuring segments 1 + + + +
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+ sortNumbers( randRangeUnique( -5, 5, 4 ) ) + [ BLUE, GREEN, PINK, ORANGE ] + randRangeUnique( 0, 4, 2 ) + [ "A", "B", "C", "D" ][ IDX_1 ] + [ "A", "B", "C", "D" ][ IDX_2 ] + POINT_1 + POINT_2 + abs( POINTS[ IDX_1 ] - POINTS[ IDX_2 ] ) +
+

What is SEGMENT?

+
+
+ init({ + range: [ [ -6, 6 ], [ -1, 1 ] ] + }); + style({ stroke: "#999" }); + line( [ -5, 0 ], [ 5, 0 ] ); + for ( var x = -5; x <= 5; x++ ) { + line( [ x, -0.2 ], [ x, 0.2 ] ); + label( [ x, -0.53 ], String( x ).replace( /-(\d)/g, "\\llap{-}\$1" ), "center", { color: "#999" } ); + } + style({ strokeWidth: 3.5 }); + line( [ 0, -0.2], [0, 0.2]); + + style({ stroke: COLORS[ 0 ], fill: COLORS[ 0 ] }); + circle( [ POINTS[ 0 ], 0 ], 0.10 ); + style({ stroke: COLORS[ 1 ], fill: COLORS[ 1 ] }); + circle( [ POINTS[ 1 ], 0 ], 0.10 ); + style({ stroke: COLORS[ 2 ], fill: COLORS[ 2 ] }); + circle( [ POINTS[ 2 ], 0 ], 0.10 ); + style({ stroke: COLORS[ 3 ], fill: COLORS[ 3 ] }); + circle( [ POINTS[ 3 ], 0 ], 0.10 ); + label( [ POINTS[ 0 ], 0 ], "A", "above", { color: COLORS[ 0 ] } ); + label( [ POINTS[ 1 ], 0 ], "B", "above", { color: COLORS[ 1 ] } ); + label( [ POINTS[ 2 ], 0 ], "C", "above", { color: COLORS[ 2 ] } ); + label( [ POINTS[ 3 ], 0 ], "D", "above", { color: COLORS[ 3 ] } ); +
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SOLUTION
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+ SEGMENT means the distance from \color{COLORS[ IDX_1 ]}{POINT_1} to + \color{COLORS[ IDX_2 ]}{POINT_2}. +

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SEGMENT = |\color{COLORS[ IDX_1 ]}{POINTS[ IDX_1 ]} - \color{COLORS[ IDX_2 ]}{POINTS[ IDX_2 ]}|

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SEGMENT = |POINTS[ IDX_1 ] - POINTS[ IDX_2 ]|

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SEGMENT = SOLUTION

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