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Index
Symbols
(inﬁnity symbol), 298
π (Pi symbol), 214–216
Numbers
3D shapes, volume of, 278–280
3-sided shapes (see triangles)
6-sided shapes (see hexagons)
7-sided shapes (see septagons)
8-sided shapes (see octagons)
9-sided shapes (see nonagons)
A
accurate construction, 108–112
acute angles, 10
acute triangles, 131, 148
altitude line, 144–145, 148
angles, 3
acute angles, 10
complementary angles, 9–10, 12–13, 47
cutting into smaller angles, 7, 46
equal angles, 30
of equilateral triangles, 176
of parallelograms, 246, 251
in regular polygons, 313–314, 318
right angles, 6, 11, 14, 46, 106
spread angle of speakers, 170–172, 174
of straight lines, 11, 46
supplementary angles, 17–18, 47
of triangles, estimating, 175–180
vertical angles, 19, 22, 47
apothem of regular polygon, 306, 308, 312, 318
arc of circle, 219–222, 234
area
of circles, 223–232, 234, 288, 310
compared to perimeter, 250, 309–310
of congruent triangles, 159
of equilateral triangles, 290–294, 318
of kites, 253–259
of parallelograms, 238–246
of rectangles, 156–162
of regular polygons, 280–282, 284, 302–310, 312, 318
of scalene triangles, 196
of sectors of a circle, 232, 234
of squares, 286
of trapezoids, 260–265
of triangles, 162–167, 202, 290–294
B
ballistics example (see homicide example)
bases of trapezoid, 262
bisecting isoceles triangles, 144–146
bounding rectangle, 157–163
this is the index 321
C
the index
center of triangle, 181–188
centroid of triangle, 182, 186–188, 202
circles
arc of, 219–222, 234
area of, 223–232, 234, 288, 310
circumcircle of regular polygon, 304, 306
circumcircle of triangle, 183
circumference of, 214–216, 234, 288
comparing to regular polygons, 303–306
diameter of, 208, 234
incircle of regular polygon, 304, 306
incircle of triangle, 182
as regular polygons, 298, 312
sectors of, 210, 226–228, 232, 234
similarity of, 77, 100
circumcenter of triangle, 183, 186, 202
circumcircle of regular polygon, 304, 306
circumcircle of triangle, 183
circumference of circle, 214–216, 234, 288
circumradius of regular polygon, 306, 308, 312, 318
complementary angles, 9–10, 12–13, 47
congruent shapes, 81–82, 89, 100
congruent triangles
area of, 159
dividing regular polygons into, 302
crime scene example (see homicide example)
cubes, volume of, 278
D
diameter of circle, 208, 234
drawings
accuracy of, 5, 8, 30
accurate construction of, 108–112
equal angles marked on, 30
parallel lines marked on, 39
right angles marked on, 6, 46
E
8-sided shapes (see octagons)
equal angles, markings for, 30
equilateral polygons (see regular polygons)
equilateral triangles
angles of, 176
area of, 290–294, 318
center of, 188
perimeter of, 294
examples (see homicide example; hot tub example; lawn
service example; myPod example; pizza example;
rock festival example; skate ramp example)
F
F patterns, in parallel lines, 40, 47
factor trees, 121, 122
fractions, compared to ratios, 94
H
Hero’s formula, 196–200, 202, 290–292
hexagons, 298, 312–316
homicide example, 2–44
angle calculations from Benny to bullet in wall, 4–23
angle calculations from Charlie to car to bullet in wall,
28–44
hot tub example, 274–317
angles in hot tub, 313–314
area of hot tub, 282
perimeter of hot tub, 284–310
side lengths of hot tub, 315–316
volume of hot tub, 278–280
hypotenuse of triangle, 131, 138
322 Index

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