INDEX. Arc Addition Postulate,


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1 # right triangle, , 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, , 142 Altitude of similar figures, 413 of a triangle, , 676 of a trapezoid, 298 AngleAngle Similarity, , 683 AngleAngleSide Postulate, , 678 AngleSideAngle Postulate, 202, 678 Angle acute, 77, 669 adjacent, 109, 669 alternate exterior, 147, 674 alternate interior, , 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, inside a circle, 509 interior, 189 interior on the same side of a transversal, 148, 674 linear pair, 109, 670 measuring, naming, obtuse, 78, 669 opposite, , 293, 306 outside a circle, 510 right, 77, , 669 straight angle, 669 supplementary, 104, 670 vertical, , 669 Apothem, Arc congruent, degree measure, defined, 486 linear measure, major, 486 midpoint of, 497 minor, 486 semicircle, 486 Arc Addition Postulate, 493 Arc LengthDegree Measure Proportion, 493 Area Area Addition Postulate, 523 defined, of a circle, , 688 of a parallelogram, , 687 of a rectangle, 523, 687 of a regular polygon, , 688 of a rhombus, , 687 of a sector of a circle, of a segment of a circle, 545 of similar figures, of a square, 533, 687 of a trapezoid, , 687 of a triangle, , 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, Betweenness of Rays, 72 Bisector angle, 82, 668 construction, 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, , defined, theorems of, Circle Arc Addition Postulate, 493 Arc LengthDegree Proportion, 493 arcs, 486, 685 area, , 688 center, 470 central angle, 487, 685 chord, , 685 congruent arcs, congruent chords, , congruent circles, 472 circumference, 492 defined, 470 diameter, 471, 685 equation of, 614 inscribed angle, , 685 major arc, 486 minor arc, 486
2 point of tangency, 471 products inside, 515, 686 products outside, , 686 Proportion of Area of Sector of a Circle, 545 radius, 470, 685 secant line, 471, 685 secant segment, sector of, 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, Compass, Complementary angles, 98, 670 Concave polygon, 172 Conclusion, Conditional statement, 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, chords, , line segments, 58 figures, 35 triangles, , 678 Congruent triangle shortcuts AngleAngleSide, , 678 AngleSideAngle, 202, 678 HypotenuseLeg, 207, 678 SideAngleSide, , 678 SideSideSide, 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, perpendicular lines, of a segment bisector, 627 Contrapositive statement, , 666 Converse of the Base Angles Theorem, 251 Converse of the definition of congruent triangles (see C.P.C.T.C), Converse of the definition of similar triangles, Converse of the Pythagorean Theorem, 426 Converse statement, , 280, 666 Convex Polygon, 172 Coordinate geometry, 586 Coordinate plane, 586 Coordinate proof using the coordinate plane, , 673 with circles, Coplanar, 136 Corollary, 185 Correspondence, Corresponding angles, 137 Corresponding Parts of Congruent Triangles are Congruent (C.P.C.T.C.), Cosine ratio (cos), 459 Crossmultiplying, Cylinder axis, 568 defined, 568 lateral surface, 568 oblique cylinder, 568 radius, 568 right cylinder, 568 volume, 568, 689 D Decagon, , 681 Deduction, 12 Deductive reasoning, 1214, 666 Degrees, 71 Degree measure of an angle, 71 of an arc, Diagonals of manyside polygons, 339 of a parallelogram, 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, on the coordinate plane, Distance Formula defined, 592, 692 in a coordinate proof, 608 Division Property of Division Property of E Each exterior angle of a regular polygon, 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, Estimating irrational numbers, 430 Euclid s Postulates, 34
3 Euler diagram, 13 Exterior Angle of a Triangle Theorem, 189, 677 Exterior Angle Inequality Theorem, , 677 Exterior angle, 189 Exterior side, 109 Extremes, F Faces, 552 Formal proof, 92, 671 G Gauss, Karl Friedrich, 641 Geometric mean, 376 Given statement, 92 Graphing, 586, , , 603, 604, 691 H Heptagon, , 681 Hexagon, , 681 Hypotenuse, 178 HypotenuseLeg Postulate, 207, 678 I If Unequal Angles, then Unequal Sides, If Unequal Sides, then Unequal Angles, 286 Included angle, Included side, Indirect proof, , 672 Induction, 6 Inductive Reasoning, 67, 666 Inequalities, Informal proof, 9293, 671 Inscribed angle, , 685 Interior angles of the same side of a transversal, 148 Interior angle, 189 Invalid reasoning, 1314, 666 Inverse statement, 280, 666 Irrational numbers defined, 430 estimating, 430 simplifying, Isosceles triangle, 178 Isosceles right triangle, , 684 Isosceles trapezoid, L Lateral faces, 557 Lateral surface of a cone, 569 of a cylinder, 568 Law of Reflection, 98 Legs of a trapezoid, Legs of a right triangle, 178 Lines defined, 44, 667 determining, 52 parallel, , 142, , 674 perpendicular, , segment, slope of, Linear equation, , 691 Linear pair, 109, 670 Line segment bisector, congruent line segments, 58 construction, defined, 58, 667 measuring, midpoint of, 81 naming, 58 Logic, , 666 Logic chain, 27 Logical Equivalence, , 666 M Major arc, 486 Minor arc, 486 Means, Measuring angles, arcs (degree measure), arcs (linear measure), area, distances, , Earth, 153 line segments, the solar system, Median of similar figures, of a triangle, , 676 of a trapezoid, Midpoint Formula defined, 592, 692 in a coordinate proof, Midpoint of a line segment, 81 of an arc, 497 Multiplication Property of Equality, 86 Multiplication Property of Inequality, N Negative reciprocal, 598 Nonagon, , 681 Noncollinear points, 51 NonEuclidian geometry, O Oblique prism, 557 Oblique cone, 569 Oblique cylinder, 568 Obtuse angle, 78, 669 Obtuse triangle, 179, 675 Octagon, , 681 Opposite angles of a quadrilateral, 293 of a triangle, of a parallelogram, 306 Opposite sides of a quadrilateral, 292 of a triangle, of a parallelogram, 310 Opposite side (trigonometry), 452 Ordered pair, 586 Origin, 586 Overlapping triangles, P Parallel lines, , 142, , 598, 674 Parallelogram area, , 687
4 consecutive angles, 305 defined, 305, 679 diagonals, opposite angles, 306 opposite sides, 310 proving, , , 680 Pentagon, Perimeter, of similar figures, of a polygon, 364 of a regular polygon, 365 Perpendicular bisector, 124, 240, 668 Perpendicular lines, , Pi, 492 Plane, 4445, 52, 667 Point of tangency, 471 Pointslope form, 603, 691 Points defined, 44, 667 collinear, 51 noncollinear, 51 Polygon concave, 172 convex, 172 decagon, , 681 defined, 172 each exterior angle, , 681 each interior angle, 358, 681 heptagon, , 681 hexagon, , 681 nonagon, , 681 quadrilateral, , 679 parallelogram, , , 679 pentagon, , 681 perimeter, rectangle, 326, 679 regular, , 681 rhombus, 326, 679 square, , 679 sum of exterior angles, , 681 sum of interior angles, , 681 trapezoid, , 679 Polyhedron, 552 Postulate, 20 Premise, Prism bases, 557 defined, 557 lateral faces, 557 nonregular, 558 oblique, 557 regular, 558 right, 557 surface area, , 689 volume, 558, 689 Proof coordinate, , , 673 direct, 27 formal, 9293, 671 indirect, , 672 informal, 9394, 671 twocolumn, 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, Substitution, 259 Subtraction, 258 Transitive, 259 Whole Greater Than Its Part, 259 Proportions defined, in a right triangle, Proportion of Area of Sector of a Circle, 545 Protractor, 71 Prove statement, 92 Proving a parallelogram, , , 680 angles congruent, 232 bisectors, C.P.C.T.C., line segments congruent, 222 lines parallel, , 223 lines perpendicular, triangles congruent, triangles isosceles, triangles similar, , , 207, 683 Pythagorean Theorem, , 684 Pythagorean Triples, Pyramid altitude, 562 base, 562 defined, 562 lateral faces, 562 nonregular pyramid, 562 regular pyramid, 562 slant height, 562 surface area, , 689 volume, 563, 689 Q Quadrant, 586 Quadrilateral defined, 292, 679 parallelogram, , rectangle, 326, 679 rhombus, 326, 679 square, , 679 trapezoid, , 679 R Radius of a circle, 470 of a regular polygon, 539 Ratio, Ray, 65, 667 Reasons, 92 Reasoning deductive, 1214, 666 inductive, 67, 666 invalid, 1314, 666 valid, 1314, 666 Rectangle area, 523, 687 defined, 326, 679 diagonals, 331 Rectangular solid defined, 552 surface area, volume, 553 Reflection, 635
5 Reflexive Property of Regular polygon apothem, area, , 688 center, 539 central angle, 539 defined, 357, 681 finding each exterior angle, , 681 finding each interior angle, 358, 681 perimeter, 365 radius, 539 Remote interior angle, Reversibility test, 51 Rhombus area, , 687 defined, 326, 679 diagonals, 331, 336 Right angle, 77, , 669 Right cone, 569 Right cylinder, 568 Right prism, 557 Right triangle right, , 684 defined, 178, 675 isosceles right, , 684 Rise over run, 597, 691 Rotation, 635 S Scalene triangle, 178, 675 Secant line, 471 Secant segment, Sector of a circle, Segment bisector defined, 8182, 668 construction, 627 Segment of a circle, 545 Selfevident truths, 20 Semicircle, 486 SideAngleSide Postulate, , 678 SideAngleSide Similarity, , 683 SideSideAngle, 207 SideSideSide Postulate, 211, 678 SideSideSide Similarity, 402, 683 Sides, 65 Similar figures altitudes, 413 area, converse of, defined, 35, 370, in the real world, medians, perimeters, proportions, Similar solids surface areas, 579 defined, 579 volumes, Similar triangle shortcuts, AngleAngle, , 683 SideAngleSide, , 683 SideSideSide, 402, 683 Simplifying irrationals, 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 Slopeintercept form, 603, 691 Solids cone, 569 cylinder, 568 faces, 552 prism, pyramid, rectangular solid, sphere, Sphere defined, 574 surface area, 574, 690 volume, 574, 690 Square area, 533, 687 defined, , 679 Statements contrapositive, converse, , 280 equivalent statement, inverse, 280 of a proof, 92 Straight angle, 669 Straight edge, 620 Substitution Property of Substitution Property of Subtraction Property of Subtraction Property of Supplementary angles, 104, 670 Surface area defined, 552 of Earth, of a prism, , 689 of a pyramid, , 689 of a rectangular solid, , 689 of similar solids, 579 of a sphere, 574, 690 Symmetric Property of T Tangent line defined, 471 theorems of, Tangent ratio (tan), Tangent segment, 482 The Parallel Postulate, 184 The Protractor Postulate, 71 The Ruler Postulate, 58 Theorem, 28 Total area, 557 Transitive Property of Transitive Property of Transformations defined, 634 reflection,635 rotation,635 translation,634 Translation, 634 Transversal, 136 Trapezoid
6 altitude, 298 area, , 687 base angles, 299 bases, 298 defined, 298, 679 diagonals, 298 isosceles trapezoid, , 679 median, 298 legs, Triangle Inequality Postulate, 264 Triangles, right triangle, acute, 178, 675 altitude, , 676 area, , 687 congruent, defined, 172 equiangular, 179, 675 equilateral, 178, 675 exterior angle, 677 included, isosceles, 178, 675 isosceles right, median, , 676 obtuse, 179, 675 opposite, overlapping, 216 right, 178, 675 scalene, 178, 675 similar, , , sum of interior angles, , 677 Trigonometry cosine ratio, 459, 684 introduction, sine ratio, 458, 684 tangent ratio, , 684 Twocolumn proof, Vertical angle, , 669 Volume of a cone, 569, 690 of a cylinder, 568, 689 defined, 553 of Earth, of a prism, 558, 689 of a pyramid, 563, 689 of a rectangular solid, 553, 689 of similar solids, of a sphere, 574, 690 W Whole Greater Than Its Part Property, 259 X xaxis, 586 xcoordinate, 586 xintercept, 691 Y yaxis, 586 ycoordinate, 586 yintercept, 603, 691 U Undefined term, 44 V Valid reasoning, 1314, 666 Venn diagram, 13 Vertex defined, 65 inside a circle, 509, 686 outside a circle, 510, 686 Vertex angle, 178
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