A

• AA (angle-angle), 125–126, 174
• AAS (angle-angle-side), 74–75, 174
• acute angle, 15
• acute triangle, 52, 55
• addition theorems, 29–33
• adjacent angles, 16
• alternate interior/exterior angles, 86
• altitude (triangle), 54–55
• Altitude-on-Hypotenuse Theorem, 128–130
• angle-angle (AA), 125–126, 174
• angle-angle-side (AAS), 74–75, 174
• angle-arc formulas, 143–147
• Angle-Bisector Theorem, 132–133
• angles
  • addition, 29–33
  • alternate interior/exterior, 10, 86, 116
  • bisection, 18–19
  • central, 138
  • complementary, 16–17, 27–29
  • corresponding, 86, 120
  • defined, 10–11
  • inscribed, 144
  • obtuse, 15
  • pairs, 16–17
  • reflex, 15
  • right, 15
  • secant-secant, 145–146
  • secant-tangent, 145–146
  • straight, 15
  • subtraction, 33–34
  • supplementary, 17, 27–29, 86
  • tangent-chord, 144
  • tangent-tangent, 145–146
  • triangle classification by, 52
  • trisection, 18–19
• angle-side-angle (ASA), 74, 174
• apothem, 114
• arcs, 138, 140–141
• area
  • circle, 140–143
  • lateral, 152–153, 155–156
  • quadrilaterals, 107–113
  • triangle, 54–57
• ASA (angle-side-angle), 74, 174
• auxiliary lines, 90–92

B

• bases, 90
• bisected chords, 136
• bisection, 18–19
• bubble logic, 26–27

C

• central angles, 138
• chains, 24–25
• Chord-Chord Power Theorem, 148–149
• chords, 135–136
• circles
  • angle-arc formulas, 143–147
  • angles, 144–146
  • arcs, 138, 140–141
  • area, 140–143
  • central angles, 138
  • Chord-Chord Power Theorem, 148–149
  • circumference formula, 140–143
  • components, 135

• equation, 168–170

• formulas, 140–147

• power theorems, 147–150

• radii, extra, 136–138

• Secant-Secant Power Theorem, 149–150
• sector area, 141–143
• segment area, 142–143

• tangents, 138–139
• Tangent-Secant Power Theorem, 149
• theorems, 136

• circumference, 140–143
• collinear points, 11
• complementary angles, 16–17, 27–29
• cone, 154
• congruent angles, 36–37, 86, 171
• congruent triangles
  • AAS (angle-angle-side), 74–75, 174
  • about, 173–174
  • ASA (angle-side-angle), 74, 174
  • CPCTC, 76–79, 174
  • defined, 69
  • equidistance theorems, 81–83
  • HLR (hypotenuse-leg-right angle), 75, 174
  • isosceles triangle theorems, 79–81
  • proving, 69–75
  • SAS (side-angle-side), 72–74, 125, 127–128, 174
  • SSS (side-side-side method), 70–71, 173
• coordinate geometry
  • circle equation, 168–170
  • coordinate plane, 161–162
  • distance, 136, 164–165
  • formulas, 166–167
  • line equations, 168
  • midpoint, 18, 165
  • slope, 162–164
• coordinate plane, 161–162
• coplanar lines, 13
• coplanar points, 11–12
• corresponding angles, 86, 120
• corresponding sides, 120–121
• CPCTC (corresponding parts of congruent triangles are congruent), 76–79, 174
• cylinder, 151–154

D

• definitions, 9–11, 25
• diagram, as element of proofs, 22
• diameter, 135
• distance formula, 136, 164–165
• division, 18, 34–36

E

• 8-15-17 triangle, 61–63

• equations. See formulas; specific equations
• equiangular, 52
• equidistance theorems, 81–83
• equilateral triangle, 51–52, 114
• exterior angles, 10, 116

F

• figure similarity, 119–124

• 5-12-13 triangle, 61–63

• flat-top figures, 151–154
• formulas. See also polygon formulas
  • angle-arc, 143–147
  • arcs, 138
  • central angles, 138
  • chord size, 136
  • circle formula, 140–143
  • circumference, 140–143
  • coordinate geometry, 166–167
  • distance, 136, 164–165
  • exterior angles, 116
  • interior angles, 10, 116
  • midpoint, 165
  • number of diagonals in an n-gon, 118
  • perpendicularity, 136
  • Pythagorean Theorem, 58–60, 161–162
  • quadrilateral area, 107–113
  • radii size, 136
  • sector area, 141–143
  • slope, 162–164
  • triangle area, 56

• 45°-45°-90° triangle (isosceles right triangle), 64–65

G

• game plan, 28–29, 42
• geometry. See also 3-D geometry; specific topics
• geometry proofs, 6–7
• givens, 21, 22, 42–43
• groups of points, 11–12

H

• height (triangle), 54–55
• HLR (hypotenuse-leg-right angle), 75, 174
• horizontal line form, 168
• horizontal lines, segments, or rays, 12
• hypotenuse, 52
• hypotenuse-leg-right angle (HLR), 75, 174

I

• if angles, then sides (isosceles triangle theorem), 79–81, 173
• if sides, then angles (isosceles triangle theorem), 79–81, 173
• if-then logic
  • about, 23
  • bubble logic, 26–27
  • chains, 24–25
  • definitions, 25
  • postulates, 25–26
  • theorems, 25–26
  • using, 43–44
• inscribed angle, 144
• interactions between coplanar lines, 13
• interior angles, 10, 116
• intersecting lines, segments, or rays, 13
• intersecting planes, 14
• isosceles right triangle (45°-45°-90° triangle), 64–65
• isosceles trapezoid, 90, 99–100
• isosceles triangles, 51–52, 79–81, 173

K

• kite
  • area formulas, 109
  • defined, 90
  • drawing in diagonals, 112–113
  • properties of, 98–99
  • proving, 104–105

L

• lateral area, 152–153, 155–156
• legs, 52, 90
• length of an arc, 140–141
• Like Divisions/Multiples Theorem, 34–36
• line equations, 168
• linear pair, 17
• lines, 9, 12–14, 90–92, 172

M

• Midline Theorem, 126–127
• midpoint, 18, 165
• multiples (like), 34–36

N

• n-gon, number of diagonals in, 118
• non-collinear points, 11
• non-coplanar lines, 14
• non-coplanar points, 12

O

• oblique lines, segments, or rays, 13
• obtuse angle, 15
• obtuse triangle, 52, 55
• one-dimensional shapes, 6
• ordered pairs, 161

P

• parallel line properties (quadrilaterals), 85–89
• parallel lines, segments, or rays, 13, 164
• parallel planes, 14
• parallel-line theorems, 172
• parallelogram
  • area formulas, 108–109
  • defined, 90
  • locating special right triangles in, 110–111
  • properties of, 93–97
  • proving, 100–103
• perpendicular bisector, 81–83
• perpendicular lines, 13, 164
• perpendicularity, 136, 139
• pi (π), 135
• planes, 10, 14
• points, 9, 11–12
• point-slope form, 168
• pointy-top figures, 154–159
• polygon formulas
  • angle, 115–117
  • area of quadrilaterals, 107–113
  • area of regular polygons, 113–115
  • diagonal, 118
• polygons, 113–115, 119–121
• postulates, 25–26
• power theorems, 147–150
• prism, 151–154
• proofs
  • addition theorems, 29–33
  • compared with shapes, 5
  • complementary angles, 16–17, 27–29
  • congruent vertical angles, 36–37, 171
  • elements, 22–23
  • filling in gaps, 49
  • game plan, 42
  • geometry, 6–7
  • givens, 22, 42–43
  • if-then logic, 23–27, 43–44
  • like multiples/divisions, 34–36
  • reasons, best, 171–174
  • reasons for using knowledge of, 7–8
  • Substitution Property, 37–39
  • subtraction theorems, 33–34
  • supplementary angles, 17, 27–29
  • tips, 45–46
  • Transitive Property, 37–39
  • working backward, 47–48
  • writing out finished proof, 49–50
• proportionality theorems, 130–133
• prove statement, 22
• pyramid, 154
• Pythagorean Theorem, 58–60, 161–162
• Pythagorean triple triangles, 60–63

Q

• quadrilaterals
  • area, 107–113
  • auxiliary lines, 90–92
  • defined, 6, 85
  • parallel line properties, 85–89
  • properties of, 93–100
  • proving, 100–105
  • special, 89–90

R

• radii/radius, 135–138, 173
• radius-tangent perpendicularity, 139
• rays, 10, 12–14
• reason column, as element of proofs, 22–23
• rectangle, 90, 96, 103–104
• reflex angle, 15
• Reflexive Property, 171
• regular polygons, area of, 113–115
• rhombus
  • defined, 90
  • properties of, 96
  • proving, 103–104
  • using triangles and ratios, 111–112
• right angle, 15
• right triangles
  • about, 57–58
  • altitudes of, 55
  • defined, 52
  • isosceles right triangle (45°-45°-90° triangle), 64–65
  • splitting, 128–130
  • 30°-60°-90° triangle, 66–68

S

• same-side interior/exterior angles, 86
• SAS (side-angle-side), 72–74, 125, 127–128, 174
• SAS~ (side-angle-side similar), 174
• scalene triangle, 51–52
• secant, 145
• secant-secant angle, 145–146
• Secant-Secant Power Theorem, 149–150
• secant-tangent angle, 145–146
• sector area, formula for, 141–143
• segments
  • addition, 29–33
  • area, 142–143
  • bisection, 18
  • defined, 9–10
  • subtraction, 33–34
  • trisection, 18
  • types, 12–14

• 7-24-25 triangle, 61–63

• shapes, 5, 6, 7–8
• side-angle-side (SAS), 72–74, 125, 127–128, 174
• side-angle-side similar (SAS~), 174
• sides, 51–52, 120–121
• side-side-side method (SSS), 70–71, 173
• side-side-side similar (SSS~), 174
• Side-Splitter Theorem, 130–132
• similarity
  • Altitude-on-Hypotenuse Theorem, 128–130
  • Angle-Bisector Theorem, 132–133
  • figures, 119–124
  • Side-Splitter Theorem, 130–132
  • triangles, 124–128, 174
• skew lines, segments, or rays, 14
• slope formula, 162–164
• slope-intercept form, 168
• spheres, 159–160
• splitting right triangles, 128–130
• square, 90, 97, 103–104
• SS method, 125, 126–127
• SSS (side-side-side method), 70–71, 173
• SSS~ (side-side-side similar), 174
• statement column, as element of proofs, 22–23
• straight angle, 15
• street-smart method, 65
• Substitution Property, 37–39
• subtraction theorems, 33–34
• supplementary angles, 17, 27–29, 86
• surface area, 152, 155, 159–160

T

• tangent-chord angle, 144
• tangents, 138–139
• Tangent-Secant Power Theorem, 149
• tangent-tangent angle, 145–146
• theorems. See specific theorems

• 30°-60°-90° triangle, 66–68
• 3-4-5 triangle, 61–63
• 3-D geometry
  • flat-top figures, 151–154
  • pointy-top figures, 154–159
  • spheres, 159–160
• 3-D (three-dimensional) shapes, 6
• 3-D (three-dimensional) space, 11

• Transitive Property, 37–39
• transversal theorems, 85–89
• trapezoid, 90, 99–100, 109
• triangle inequality principle, 53–54
• triangles. See also congruent triangles; right triangles
  • acute, 52, 55
  • area, 54–57
  • classifications based on angles, 52
  • classifications based on sides, 51–52
  • congruence, 173–174
  • 8-15-17, 61–63
  • equilateral, 51–52, 114
  • 5-12-13, 61–63
  • height, 54–55
  • isosceles, 51–52
  • isosceles right triangle (45°-45°-90° triangle), 64–65
  • obtuse, 52, 55
  • proving similar, 124–128
  • Pythagorean Theorem, 58–60
  • Pythagorean triple triangles, 60–63
  • scalene, 51–52
  • 7-24-25, 61–63
  • similarity, 124–128, 174
  • 30°-60°-90° triangle, 66–68
  • 3-4-5, 61–63
  • triangle inequality principle, 53–54
• trisection, 18–19

• 2-D (two-dimensional) shapes, 6

V

• vertex, 10
• vertical angle theorem, 171
• vertical angles, 17, 36–37
• vertical line form, 168
• vertical lines, segments, or rays, 12
• volume, 152, 155, 159–160

W

• writing out finished proofs, 49–50

X

• x-coordinate, 161

Y

• y-coordinate, 161