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INDEX
#
30-60 right triangle, 441442, 684
A
Absolute value, 59
Acute angle, 77, 669
Acute triangle, 178
Addition Property of
Equality, 86
Addition Property of
Inequality, 258
Adjacent angle, 109, 669
Adjacent side
(trigonometry), 452
Alternate exterior angle,
147
Alternate interior angle,
136-137, 142
Altitude
of similar figures, 413
of a triangle, 239-240,
676
of a trapezoid, 298
Angle-Angle Similarity,
396-397, 683
Angle-Angle-Side Postulate,
202-203, 678
Angle-Side-Angle Postulate,
202, 678
Angle
acute, 77, 669
adjacent, 109, 669
alternate exterior, 147,
674
alternate interior, 136137, 142, 674
bisector, 82, 627, 668
central, 487
common, 216
complementary, 98, 670
congruent, 71
consecutive, 293, 305
construction, 621
corresponding, 137, 142,
674
defined, 65
exterior, 189
inscribed, 503-504
inside a circle, 509
interior, 189
interior on the same side
of a transversal, 148, 674
linear pair, 109, 670
measuring, 71-72
naming, 65-66
obtuse, 78, 669
opposite, 172-173, 293,
306
outside a circle, 510
right, 77, 119-120, 669
straight angle, 669
supplementary, 104, 670
vertical, 113-114, 669
Apothem, 539-540
Arc
congruent, 497-499
degree measure, 486-488
defined, 486
linear measure, 492-493
major, 486
midpoint of, 497
minor, 486
semicircle, 486
Arc Addition Postulate, 493
Arc Length-Degree
Measure Proportion,
493
Area
Area Addition Postulate,
523
defined, 522-523
of a circle, 544-545, 688
of a parallelogram, 528529, 687
of a rectangle, 523, 687
of a regular polygon,
539-540, 688
of a rhombus, 533-534,
687
of a sector of a circle,
544-545
of a segment of a circle,
545
of similar figures, 545546
of a square, 533, 687
of a trapezoid, 534-535,
687
of a triangle, 527-528,
687
Area Addition Postulate,
523
Auxiliary lines, 184
Axis
of a cone, 569
of a cylinder, 568
B
Bases
of a prism, 557
of a trapezoid, 298
of an isosceles triangle,
178
Base Angles
of a trapezoid, 299
of a triangle, 246, 677
Base Angles Theorem, 246
Betweenness of Points, 5960
Betweenness of Rays, 72
Bisector
angle, 82, 668
construction, 627-628
perpendicular, 124, 240,
668
segment, 81, 668
C
Center
of a circle, 470, 685
of a regular polygon, 539
Central angle
of a circle, 487, 685
of a regular polygon, 539
Chords
bisecting, 475
congruent, 475-476, 497499
defined, 470-471
theorems of, 475-476
Circle
Arc Addition Postulate,
493
Arc Length-Degree
Proportion, 493
arcs, 486, 685
area, 544-545, 688
center, 470
central angle, 487, 685
chord, 470-471, 685
congruent arcs, 497-499
congruent chords, 475476, 497-499
congruent circles, 472
circumference, 492
defined, 470
diameter, 471, 685
equation of, 614
inscribed angle, 503-504,
685
major arc, 486
minor arc, 486
INDEX
point of tangency, 471
products inside, 515, 686
products outside, 515516, 686
Proportion of Area of
Sector of a Circle, 545
radius, 470, 685
secant line, 471, 685
secant segment, 515-516
sector of, 544-545
segment of, 545
semicircle, 486
similar circles, 472
tangent line, 471, 685
tangent segment, 482
vertex inside, 509, 686
vertex outside, 510, 686
Circumference, 492
Collinear points, 51
Common angle, 216
Common side, 216-217
Compass, 620-621
Complementary angles, 98,
670
Concave polygon, 172
Conclusion, 12-13
Conditional statement, 1213
Cone
axis, 569
base of, 569
defined, 569
lateral surface, 569
oblique cone, 569
right cone, 569
slant height, 569
vertex, 569
volume, 569, 690
Congruent
angles, 71
arcs, 497-499
chords, 475-476, 497499
line segments, 58
figures, 35
triangles, 193-194, 678
Congruent triangle
shortcuts
Angle-Angle-Side, 202203, 678
Angle-Side-Angle, 202,
678
Hypotenuse-Leg, 207,
678
Side-Angle-Side, 198199, 678
Side-Side-Side, 211, 678
Consecutive angles, 293,
305
Consecutive sides, 292
Construction
of an angle, 621
of an angle bisector, 627
impossible constructions,
628
of a line segment, 620621
perpendicular lines, 627628
of a segment bisector,
627
Contrapositive statement,
281-282, 666
Converse of the Base
Angles Theorem, 251
Converse of the definition
of congruent triangles
(see C.P.C.T.C), 222-232
Converse of the definition
of similar triangles,
407-409
Converse of the
Pythagorean Theorem,
426
Converse statement, 158160, 280, 666
Convex Polygon, 172
Coordinate geometry, 586
Coordinate plane, 586
Coordinate proof
using the coordinate
plane, 608-609, 673
with circles, 614-615
Coplanar, 136
Corollary, 185
Correspondence,
Corresponding angles, 137
Corresponding Parts of
Congruent Triangles
are Congruent
(C.P.C.T.C.), 222-232
Cosine ratio (cos), 459
Cross-multiplying, 376-377
Cylinder
axis, 568
defined, 568
lateral surface, 568
oblique cylinder, 568
radius, 568
right cylinder, 568
volume, 568, 689
D
Decagon, 338-339, 681
Deduction, 12
Deductive reasoning, 12-14,
666
Degrees, 71
Degree measure
of an angle, 71
of an arc, 486-488
Diagonals
of many-side polygons,
339
of a parallelogram, 310311
of a quadrilateral, 293
of a rectangle, 331
of a rhombus, 331, 336
of a trapezoid,
Diameter, 470, 685
Direct proof, 27
Distance
of line segments, 130131
on the coordinate plane,
591-592
Distance Formula
defined, 592, 692
in a coordinate proof,
608
Division Property of
Equality, 87
Division Property of
Inequality, 259
E
Each exterior angle of a
regular polygon, 358359
Each interior angle of a
regular polygon, 358
Einstein, Albert, 641
End point
of a line segment, 58
of a ray, 65
Equation of a circle, 614
Equiangular triangle, 179,
675
Equilateral triangle, 178,
675
Equivalent figures, 35, 522
Equivalent statements, 281282
Estimating irrational
numbers, 430
Euclid’s Postulates, 34
INDEX
Euler diagram, 13
Exterior Angle of a
Triangle Theorem, 189,
677
Exterior Angle Inequality
Theorem, 269-270, 677
Exterior angle, 189
Exterior side, 109
Extremes, 375-376
F
Faces, 552
Formal proof, 92, 671
G
Gauss, Karl Friedrich, 641
Geometric mean, 376
Given statement, 92
Graphing, 586, 591-592,
597-598, 603, 604, 691
H
Heptagon, 338-339, 681
Hexagon, 338-339, 681
Hypotenuse, 178
Hypotenuse-Leg Postulate,
207, 678
I
If Unequal Angles, then
Unequal Sides, 286-287
If Unequal Sides, then
Unequal Angles, 286
Included angle, 172-173
Included side, 172-173
Indirect proof, 273-274, 672
Induction, 6
Inductive Reasoning, 6-7,
666
Inequalities, 258-259
Informal proof, 92-93, 671
Inscribed angle, 503-504,
685
Interior angles of the same
side of a transversal,
148
Interior angle, 189
Invalid reasoning, 13-14,
666
Inverse statement, 280, 666
Irrational numbers
defined, 430
estimating, 430
simplifying, 430-431
Isosceles triangle, 178
Isosceles right triangle, 436437, 684
Isosceles trapezoid, 298-299
L
Lateral faces, 557
Lateral surface
of a cone, 569
of a cylinder, 568
Law of Reflection, 98
Legs of a trapezoid, 298-299
Legs of a right triangle, 178
Lines
defined, 44, 667
determining, 52
parallel, 136-137, 142,
147-149, 674
perpendicular, 119-120,
124-125
segment,
slope of,
Linear equation, 603-604,
691
Linear pair, 109, 670
Line segment
bisector, 81-82
congruent line segments,
58
construction, 620-621
defined, 58, 667
measuring, 58-60
midpoint of, 81
naming, 58
Logic, 280-282, 666
Logic chain, 27
Logical Equivalence, 281282, 666
M
Major arc, 486
Minor arc, 486
Means, 275-276
Measuring
angles, 71-72
arcs (degree measure),
486-488
arcs (linear measure),
492-493
area, 522-523
distances, 130-131, 591592
Earth, 153
line segments, 58-60
the solar system, 463464
Median
of similar figures, 413414
of a triangle, 239-240,
676
of a trapezoid, 239-240
Midpoint Formula
defined, 592, 692
in a coordinate proof,
608-609
Midpoint
of a line segment, 81
of an arc, 497
Multiplication Property of
Equality, 86
Multiplication Property of
Inequality, 258-259
N
Negative reciprocal, 598
Nonagon, 338-339, 681
Noncollinear points, 51
Non-Euclidian geometry,
640-641
O
Oblique prism, 557
Oblique cone, 569
Oblique cylinder, 568
Obtuse angle, 78, 669
Obtuse triangle, 179, 675
Octagon, 338-339, 681
Opposite angles
of a quadrilateral, 293
of a triangle, 172-173
of a parallelogram, 306
Opposite sides
of a quadrilateral, 292
of a triangle, 172-173
of a parallelogram, 310
Opposite side
(trigonometry), 452
Ordered pair, 586
Origin, 586
Overlapping triangles, 216217
P
Parallel lines, 136-137, 142,
147-149, 598, 674
Parallelogram
area, 528-529, 687
INDEX
consecutive angles, 305
defined, 305, 679
diagonals, 310-311
opposite angles, 306
opposite sides, 310
proving, 315-317, 321322, 680
Pentagon, 338-339
Perimeter,
of similar figures, 414415
of a polygon, 364
of a regular polygon, 365
Perpendicular bisector, 124,
240, 668
Perpendicular lines, 119120, 124-125
Pi, 492
Plane, 44-45, 52, 667
Point of tangency, 471
Point-slope form, 603, 691
Points
defined, 44, 667
collinear, 51
noncollinear, 51
Polygon
concave, 172
convex, 172
decagon, 338-339, 681
defined, 172
each exterior angle, 358359, 681
each interior angle, 358,
681
heptagon, 338-339, 681
hexagon, 338-339, 681
nonagon, 338-339, 681
quadrilateral, 292-293,
679
parallelogram, 305-306,
310-311, 679
pentagon, 338-339, 681
perimeter, 364-365
rectangle, 326, 679
regular, 357-359, 681
rhombus, 326, 679
square, 326-327, 679
sum of exterior angles,
352-353, 681
sum of interior angles,
346-347, 681
trapezoid, 298-299, 679
Polyhedron, 552
Postulate, 20
Premise, 12-13
Prism
bases, 557
defined, 557
lateral faces, 557
non-regular, 558
oblique, 557
regular, 558
right, 557
surface area, 557-558,
689
volume, 558, 689
Proof
coordinate, 608-609,
614-615, 673
direct, 27
formal, 92-93, 671
indirect, 273-274, 672
informal, 93-94, 671
two-column, 92-93
Properties of Equality
Addition, 86
Division, 87
Multiplication, 86
Reflexive, 87
Substitution, 87
Subtraction, 86
Symmetric, 87
Transitive, 87
Properties of Inequality
Addition, 258
Division, 259
Multiplication, 258-259
Substitution, 259
Subtraction, 258
Transitive, 259
Whole Greater Than Its
Part, 259
Proportions
defined, 375-377
in a right triangle, 420421
Proportion of Area of
Sector of a Circle, 545
Protractor, 71
Prove statement, 92
Proving
a parallelogram, 315317, 321-322, 680
angles congruent, 232
bisectors, 228-229
C.P.C.T.C., 222-223
line segments congruent,
222
lines parallel, 165-166,
223
lines perpendicular, 223224
triangles congruent, 211212
triangles isosceles, 251252
triangles similar, 198199, 202-203, 207, 683
Pythagorean Theorem, 425426, 684
Pythagorean Triples, 431431
Pyramid
altitude, 562
base, 562
defined, 562
lateral faces, 562
non-regular pyramid,
562
regular pyramid, 562
slant height, 562
surface area, 562-563,
689
volume, 563, 689
Q
Quadrant, 586
Quadrilateral
defined, 292, 679
parallelogram, 305-306,
310-311
rectangle, 326, 679
rhombus, 326, 679
square, 326-327, 679
trapezoid, 298-299, 679
R
Radius
of a circle, 470
of a regular polygon, 539
Ratio, 370-371
Ray, 65, 667
Reasons, 92
Reasoning
deductive, 12-14, 666
inductive, 6-7, 666
invalid, 13-14, 666
valid, 13-14, 666
Rectangle
area, 523, 687
defined, 326, 679
diagonals, 331
Rectangular solid
defined, 552
surface area, 552-553
volume, 553
Reflection, 635
INDEX
Reflexive Property of
Equality, 87
Regular polygon
apothem, 539-540
area, 539-540, 688
center, 539
central angle, 539
defined, 357, 681
finding each exterior
angle, 358-359, 681
finding each interior
angle, 358, 681
perimeter, 365
radius, 539
Remote interior angle,
Reversibility test, 51
Rhombus
area, 533-534, 687
defined, 326, 679
diagonals, 331, 336
Right angle, 77, 119-120,
669
Right cone, 569
Right cylinder, 568
Right prism, 557
Right triangle
30-60 right, 441-442,
684
defined, 178, 675
isosceles right, 436-437,
684
Rise over run, 597, 691
Rotation, 635
S
Scalene triangle, 178, 675
Secant line, 471
Secant segment,
Sector of a circle, 544-545
Segment bisector
defined, 81-82, 668
construction, 627
Segment of a circle, 545
Self-evident truths, 20
Semicircle, 486
Side-Angle-Side Postulate,
198-199, 678
Side-Angle-Side Similarity,
401-402, 683
Side-Side-Angle, 207
Side-Side-Side Postulate,
211, 678
Side-Side-Side Similarity,
402, 683
Sides, 65
Similar figures
altitudes, 413
area, 545-546
converse of, 407-409
defined, 35, 370, 380382
in the real world, 286287
medians, 413-414
perimeters, 414-415
proportions, 380-382
Similar solids
surface areas, 579
defined, 579
volumes, 579-580
Similar triangle shortcuts,
Angle-Angle, 396-397,
683
Side-Angle-Side, 401402, 683
Side-Side-Side, 402, 683
Simplifying irrationals,
430-431
Sine ration (sin), 458
Slant height
of a cone, 569
of a cylinder, 568
Slope
defined, 597, 691
of horizontal lines, 598,
691
of parallel lines, 598,
692
of perpendicular lines,
598, 692
of vertical lines, 598,
692
Slope-intercept form, 603,
691
Solids
cone, 569
cylinder, 568
faces, 552
prism, 557-558
pyramid, 562-563
rectangular solid, 552553
sphere, 574-575
Sphere
defined, 574
surface area, 574, 690
volume, 574, 690
Square
area, 533, 687
defined, 326-327, 679
Statements
contrapositive, 280-281
converse, 158-160, 280
equivalent statement,
281-282
inverse, 280
of a proof, 92
Straight angle, 669
Straight edge, 620
Substitution Property of
Equality, 87
Substitution Property of
Inequality, 259
Subtraction Property of
Equality, 87
Subtraction Property of
Inequality, 259
Supplementary angles, 104,
670
Surface area
defined, 552
of Earth, 574-575
of a prism, 557-558, 689
of a pyramid, 562-563,
689
of a rectangular solid,
552-553, 689
of similar solids, 579
of a sphere, 574, 690
Symmetric Property of
Equality, 87
T
Tangent line
defined, 471
theorems of, 481-482
Tangent ratio (tan), 452-454
Tangent segment, 482
The Parallel Postulate, 184
The Protractor Postulate,
71
The Ruler Postulate, 58
Theorem, 28
Total area, 557
Transitive Property of
Equality, 87
Transitive Property of
Inequality, 259
Transformations
defined, 634
reflection,635
rotation,635
translation,634
Translation, 634
Transversal, 136
Trapezoid
INDEX
altitude, 298
area, 534-535, 687
base angles, 299
bases, 298
defined, 298, 679
diagonals, 298
isosceles trapezoid, 298299, 679
median, 298
legs, 298-299
Triangle Inequality
Postulate, 264
Triangles,
30-60 right triangle, 441442
acute, 178, 675
altitude, 239-240, 676
area, 527-528, 687
congruent, 193-194
defined, 172
equiangular, 179, 675
equilateral, 178, 675
exterior angle, 677
included, 172-173
isosceles, 178, 675
isosceles right, 436-437
median, 239-240, 676
obtuse, 179, 675
opposite, 172-173
overlapping, 216
right, 178, 675
scalene, 178, 675
similar, 380-382, 396397, 401-402
sum of interior angles,
184-185, 677
Trigonometry
cosine ratio, 459, 684
introduction, 447-449
sine ratio, 458, 684
tangent ratio, 452-454,
684
Two-column proof, 92-93
U
Undefined term, 44
V
Valid reasoning, 13-14, 666
Venn diagram, 13
Vertex
defined, 65
inside a circle, 509, 686
outside a circle, 510, 686
Vertex angle, 178
Vertical angle, 113-114, 669
Volume
of a cone, 569, 690
of a cylinder, 568, 689
defined, 553
of Earth, 574-575
of a prism, 558, 689
of a pyramid, 563, 689
of a rectangular solid,
553, 689
of similar solids, 579580
of a sphere, 574, 690
W
Whole Greater Than Its
Part Property, 259
X
x-axis, 586
x-coordinate, 586
x-intercept, 691
Y
y-axis, 586
y-coordinate, 586
y-intercept, 603, 691
INDEX