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tutorbot5.html
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tutorbot5.html
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<!DOCTYPE html>
<html>
<head>
<title>tutorbot</title>
<link rel="stylesheet" href="tutorbot.css" media="screen">
<link rel="stylesheet" type="text/css" href="jsxgraph.css" />
<link rel="stylesheet" type="text/css" href="tutorbot.css" />
<script type="text/javascript" src="jsxgraphcore.js"></script>
</head>
<body>
<div id="box" style="float:left;width:400px; height:400px;">
</div>
<div id = "solutionbox" style= "width:50%;float:left;margin-left:7%">
<div class = "pullleft width7">
Given:
</div>
<div class = "pullleft">
ABCD is a parallelogram
</div>
<hr style = "clear:both;"/>
<div class = "pullleft width7">
To Prove:
</div>
<div class = "pullleft">
ABCD is a rhombus
</div>
<hr style = "clear:both;"/>
<div class = "pullleft width7">
Proof:
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AB = CD
<br/>
and<br/> AD = BC
<br/>
</div>
<div class = "reasondiv">
opposite sides of parallelogram ABCD
</div>
<hr style = "clear:both;"/>
<span class = "smallertext">
So we need to prove that adjacent sides of ABCD are equal as well.
if we prove that AB = AD and CD = CB then all sides of ABCD are equal
and ABCD will be proved to be rhombus.
</span>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AP = AS = x<br/>
SD = DR = y<br/>
PB = BQ = a<br/>
CR = CQ = b<br/>
</div>
<div class = "reasondiv">
External Tangents from a point to circle are equal.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AB = AP + PB = x + a<br/>
AD = AS + SD = x + y<br/>
So, to prove AB = AD => we will need to prove a = y
</div>
<div class = "reasondiv">
From point 1 and 2 above.<br/>
and <br/>
Points A,P,B are collinear.<br/>
Points A,S,D are collinear.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
In △ POB and △ DOR,<br/><br/>
∠BPO = ∠DRO<br/>
PO = RO<br/>
∠POB = ∠DOR<br/>
∴ △ POB ≅ △ DOR
<br/><br/>
</div>
<div class = "reasondiv">
<br/><br/>
Radius Tangent relation.<br/>
Radii of same circle.<br/>
Vertically opposite angles, AB || CD<br/>
ASA test of congruence.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
∴ DR = PB , <br/>
∴ y = a,
</div>
<div class = "reasondiv">
Corresponding sides of congruent triangles.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
x+y = x+a<br/>
AD = AB
<br/><br/>
</div>
<div class = "reasondiv">
Add x on both sides.<br/>
AD = x + y, AB = x+a <br/>From point 4
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
Similarly , we can prove CD = BC
<br/>
AB = AD = CD = BC
</div>
<div class = "reasondiv"></div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
ABCD is a rhombus
</div>
<div class = "reasondiv">
since all sides are equal.
</div>
<hr style = "clear:both;"/>
<br/><br/>
</div>
<!-- solutionbox ends above -->
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var board = JXG.JSXGraph.initBoard('box',{axis:false, showNavigation:false, showCopyright:false});
var o = board.create('point', [0.0, 0.0],{name:'O'});
var circle = board.create('circle', [o, 3]);
var p = board.create('glider', [0.0,3.0,circle],{name:'P'});
var q = board.create('glider', [0.0,-3.0,circle],{name:'Q'});
var l1 = board.create('segment', [p, q]);
var c = board.create('glider', [3.0,-0.2,circle],{name:'C'});
var t1 = board.create('tangent', [p]);
var t2 = board.create('tangent', [q]);
var t3 = board.create('tangent', [c]);
var a = board.create('point', [3.2, 3.0],{name:'A'});
var b = board.create('point', [2.8, -3.0],{name:'B'});
var l2 = board.create('segment', [o,a]);
var l3 = board.create('segment', [o,b]);
// var r = board.create('glider', [0.0,-3.0,circle],{name:'R'});
// var q = board.create('glider', [3.0,0.0,circle],{name:'Q'});
// var p = board.create('glider', [0.0,3.0,circle],{name:'P'});
// var s = board.create('glider', [-3.0,0.0,circle],{name:'S'});
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// var t2 = board.create('tangent', [q]);
// var t3 = board.create('tangent', [r]);
// var t4 = board.create('tangent', [s]);
// var a = board.create('point', [-3.0, 3.0],{name:'A'});
// var b = board.create('point', [3.0, 3.0],{name:'B'});
// var c = board.create('point', [3.0, -3.0],{name:'C'});
// var d = board.create('point', [-3.0,-3.0],{name:'D'});
// var l1 = board.create('segment', [p, r]);
// var l2 = board.create('segment', [b, d]);
// var l2 = board.create('segment', [a, c]);
</script>
</body>
</html>