This repository has been archived by the owner on May 11, 2021. It is now read-only.
/
congruent_triangles_2.html
218 lines (210 loc) · 11.2 KB
/
congruent_triangles_2.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
<!DOCTYPE html>
<html data-require="math graphie graphie-helpers graphie-geometry math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Congruent triangles 2</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<p class="question">
What is the value of the angle <code>x</code>?
</p>
<div class="vars" data-ensure="TR_A.niceSideLengths[0] !== TR_A.niceSideLengths[2]">
<var id="RAND_ANG">rand(3)</var>
<var id="NEW_ANG">""</var>
<var id="ANGLE_LABELS">["CAB", "ABC", "BCA"]</var>
<var id="ANG_FIRST">""</var>
<var id="ANG_LEFT">""</var>
<var id="ANGLES">randomTriangleAngles.triangle()</var>
<var id="ANG">""</var>
<var id="ANGLES_A">[RAND_ANG]</var>
<var id="ANGLES_B">clearArray(["x", "x", "x"], [RAND_ANG])</var>
<var id="SIDES_A">[0, 2]</var>
<var id="SIDES_B">[0, 2]</var>
<var id="TR_A">
function(){
var trA = new Triangle([0, 0], ANGLES, 8, {});
trA.labels = {
"points": ["A", "B", "C"],
"sides": clearArray(trA.niceSideLengths, SIDES_A),
"angles": clearArray(trA.niceAngles, ANGLES_A)
};
return trA;
}()
</var>
<var id="TR_B">
function(){
var trB = new Triangle( [ TR_A.centroid[ 0 ], TR_A.centroid[ 1 ] ], ANGLES, 8, {} );
trB.rotate( 180 );
trB.labels = { "points" : [ "D", "", "" ], "sides" : clearArray( trB.niceSideLengths, SIDES_B ),"angles" : ANGLES_B };
return trB;
}()
</var>
<var id="ANSWER">ANGLES[ RAND_ANG ]</var>
</div>
<p class="render-answer-area-here"></p>
<div class="problem">
<div class="graphie" id="triangle">
var minX = min(0, min(TR_A.points[1][0], TR_A.points[2][0]));
var maxX = TR_A.points[1][0] + max(0, TR_A.points[2][0]);
var scale = min(60, 400 / (maxX - minX + 2));
init({
range: [[minX - 1, maxX + 1], [-1, TR_A.points[2][1] + 1]],
scale: scale
})
TR_A.draw();
TR_A.drawLabels();
TR_B.draw();
TR_B.drawLabels();
</div>
</div>
<div class="solution" data-type="multiple">
<p><code>x = </code> <span class="sol short40" data-type="number"><var>ANSWER</var></span> <code>^\circ</code></p>
</div>
<div class="problems">
<div id="parr">
<div class="vars">
<var id="ANG_FIRST">randRangeUnique(0, 2, 2)</var>
<var id="ANG_LEFT">randFromArray(ANG_FIRST)</var>
<var id="ANGLES_A">ANG_FIRST</var>
<var id="ANGLES_B">clearArray(["x", "x", "x"], [ANG_LEFT])</var>
<var id="ANSWER">TR_B.angles[ANG_LEFT]</var>
</div>
<div class="hints">
<p>
<code>\triangle ABC</code> and <code>\triangle BCD</code> have three sides equal.<br>
They share side <code>BC</code>.<br>
<code>AB = CD</code><br>
<code>AC = BD</code>
</p>
<p>Therefore <code>\triangle ABC</code> and <code>\triangle BCD</code> are congruent.</p>
<p>Congruent triangles also have congruent (equal) angles.</p>
<p>
If we superimpose these two triangles, by rotating <code>\triangle ABC</code>,
we see that angle <code>x</code> corresponds to <code>\angle <var>ANGLE_LABELS[ANG_LEFT]</var></code>.
</p>
<p>Angle <code>x</code> is therefore equal to <code><var>ANSWER</var>^\circ</code>.</p>
</div>
</div>
<div id="parr2">
<div class="vars">
<var id="ANG_FIRST">randRangeUnique( 0, 2, 2 )</var>
<var id="ANG_LEFT">randRangeExclude( 0, 2, ANG_FIRST )</var>
<var id="ANGLES_A">ANG_FIRST</var>
<var id="ANGLES_B">clearArray( [ "x", "x", "x" ], [ ANG_LEFT ] )</var>
<var id="ANSWER">TR_B.angles[ANG_LEFT]</var>
</div>
<div class="solution" data-type="multiple">
<p><code>x = </code> <span class="sol short40" data-type="number"><var>ANSWER</var></span> <code>^\circ</code></p>
</div>
<div class="hints">
<p>
<code>\triangle ABC</code> and <code>\triangle BCD</code> have three sides equal.<br>
They share side <code>BC</code>.<br>
<code>AB = CD</code><br>
<code>AC = BD</code>
</p>
<p>Therefore <code>\triangle ABC</code> and <code>\triangle BCD</code> are congruent.</p>
<p>Congruent triangles also have congruent (equal) angles.</p>
<p>
If we superimpose these two triangles, by rotating <code>\triangle ABC</code>,
we see that angle <code>x</code> corresponds to <code>\angle <var>ANGLE_LABELS[ANG_LEFT]</var></code>.
</p>
<p><code>
<var>ANGLE_LABELS[ANG_LEFT]</var> = 180^\circ - <var>TR_A.angles[ANG_FIRST[0]]</var>^\circ - <var>TR_A.angles[ANG_FIRST[1]]</var>^\circ
</code></p>
<div>
<p><code><var>ANGLE_LABELS[ ANG_LEFT ]</var> = x = <var>ANSWER</var>^\circ</code></p>
<div class="graphie" data-update="triangle">
TR_A.labels.angles = TR_A.niceAngles;
TR_A.labels = {"angles" : clearArray(TR_A.niceAngles, [ANG_LEFT])};
TR_A.drawLabels();
</div>
</div>
</div>
</div>
<div id="opposite">
<div class="vars" data-ensure="TR_A.niceSideLengths[0] !== TR_A.niceSideLengths[2]">
<var id="NEW_ANG">RAND_ANG === 2 ? 2 : 1 - RAND_ANG</var>
<var id="SIDES_B">[0, 1]</var>
<var id="ANG_FIRST">randRangeUnique(0, 2, 2)</var>
<var id="ANG_LEFT">randFromArray([0, 2])</var>
<var id="SHOW_ANGLE">ANG_LEFT === 2 ? 2 : 1 - ANG_LEFT</var>
<var id="SAME_ANGLE">($.inArray( SHOW_ANGLE, ANG_FIRST) !== -1)</var>
<var id="ANGLES_A">ANG_FIRST</var>
<var id="ANGLES_B">clearArray(["x", "x", "x"], [ANG_LEFT])</var>
<var id="ANG">ANGLES[0] / 2</var>
<var id="TR_A">
function(){
var trA = new Triangle([0, 0], ANGLES ,6, {});
trA.rotationCenter = trA.points[0];
trA.rotate(ANG);
trA.labels = {
"points": ["", "B", "C"],
"sides": clearArray(trA.niceSideLengths, SIDES_A),
"angles": clearArray(trA.niceAngles, ANGLES_A)
};
return trA;
}()
</var>
<var id="TR_B">
function(){
var rad = ANG * PI / 180;
var trB = new Triangle([-cos(rad) * TR_A.sideLengths[0], -sin(rad) * TR_A.sideLengths[0]], [ANGLES[1], ANGLES[0], ANGLES[2]], 6, {});
trB.rotationCenter = trB.points[0];
trB.rotate(-ANG);
trB.labels = { "points" : [ "D", "", "E" ], "sides" : clearArray( trB.niceSideLengths, SIDES_B ), "angles" : ANGLES_B };
return trB;
}()
</var>
<var id="ANSWER">TR_B.angles[ANG_LEFT]</var>
</div>
<div class="problem">
<div class="graphie" id="oppTriangle">
var maxX = max(TR_A.points[1][0], TR_A.points[2][0]) + 1;
var minY = TR_A.points[1][1] - 1;
var maxY = TR_A.points[2][1] + 1;
var scale = min(500 / (maxY - minY), 220 / maxX);
init({
range: [[-maxX, maxX], [minY, maxY]],
scale: scale
})
TR_A.draw();
TR_A.drawLabels();
TR_B.draw();
TR_B.drawLabels();
label(TR_B.points[1], "A", "above");
</div>
</div>
<div class="solution" data-type="multiple">
<p><code>x = </code> <span class="sol short40" data-type="number"><var>ANSWER</var></span> <code>^\circ</code></p>
</div>
<div class="hints">
<p><code>\angle DAE</code> forms a vertical angle with <code>\angle BAC</code>, so <code>\angle DAE = \angle BAC</code>.</p>
<p><code>\triangle ABC</code> and <code>\triangle ADE</code> also have two sides equal.</p>
<p>Therefore <code>\triangle ABC</code> and <code>\triangle ADE</code> are congruent.</p>
<p>Congruent triangles also have congruent (equal) angles.</p>
<p>
If we superimpose these two triangles, by flipping <code>\triangle EDA</code>,
we see that angle <code>x</code> corresponds to <code>\angle <var>ANGLE_LABELS[SHOW_ANGLE]</var></code>.
</p>
<div data-if="!SAME_ANGLE">
<p><code>
<var>ANGLE_LABELS[SHOW_ANGLE]</var> = 180 - <var>TR_A.angles[ANG_FIRST[0]]</var> - <var>TR_A.angles[ANG_FIRST[1]]</var>
</code></p>
<div class="graphie" data-update="oppTriangle">
TR_A.labels.angles = TR_A.niceAngles;
TR_B.labels.angles = mergeArray(TR_B.labels.angles, [TR_A.niceAngles[1], TR_A.niceAngles[0], TR_A.niceAngles[2]]);
TR_A.drawLabels();
TR_B.drawLabels();
</div>
<p><code><var>ANGLE_LABELS[SHOW_ANGLE]</var> = x = <var>TR_B.angles[ANG_LEFT]</var></code></p>
</div>
<p>Angle <code>x</code> is therefore equal to <code><var>ANSWER</var>^\circ</code>.</p>
</div>
</div>
</div>
</div>
</body>
</html>