Index

Symbols

∞ (inﬁnity symbol), 298

π (Pi symbol), 214–216

Numbers

3D shapes, volume of, 278–280

3-sided shapes (see triangles)

4-sided shapes (see quadrilaterals; squares)

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

adjacent angles, 9

altitude line, 144–145, 148

angles, 3

acute angles, 10

adding, 7–10

adjacent angles, 9

complementary angles, 9–10, 12–13, 47

cutting into smaller angles, 7, 46

equal angles, 30

of equilateral triangles, 176

of parallelograms, 246, 251

of quadrilaterals, adding, 34–37, 46

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, adding, 20–22, 46

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

radius of, 208, 234

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

(see also regular polygons)

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

4-sided shapes (see quadrilaterals; squares)

fractions, compared to ratios, 94

H

Hero’s formula, 196–200, 202, 290–292

hexagons, 298, 312–316

(see also regular polygons)

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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