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High School Mathematics Geometry Vocabulary Word Wall Cards Table of Contents Reasoning, Lines, and Transformations Basics of Geometry 1 Basics of Geometry 2 Geometry Notation Conditional Statement Converse Inverse Symbolic Representations Deductive Reasoning Inductive Reasoning Proof Properties of Congruence Counterexample Perpendicular Lines Parallel Lines Transversal Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles Parallel Lines Midpoint Midpoint Formula Slope Formula Slope of Lines in Coordinate Plane Distance Formula Line Symmetry Point Symmetry Rotation (Origin) (back to top) Reflection Translation Dilation Rotation (Point) Perpendicular Bisector Constructions: o A line segment congruent to a given line segment o Perpendicular bisector of a line segment o A perpendicular to a given line from a point not on the line o A perpendicular to a given line at a point on the line o A bisector of an angle o An angle congruent to a given angle o A line parallel to a given line through a point not on the given line o An equilateral triangle inscribed in a circle o A square inscribed in a circle o A regular hexagon inscribed in a circle o An inscribed circle of a triangle o A circumscribed circle of a triangle Triangles Classifying Triangles by Sides Classifying Triangles by Angles Triangle Sum Theorem Exterior Angle Theorem Geometry Vocabulary Cards Page 1 Pythagorean Theorem Angle and Sides Relationships Triangle Inequality Theorem Congruent Triangles SSS Triangle Congruence Postulate SAS Triangle Congruence Postulate HL Right Triangle Congruence ASA Triangle Congruence Postulate AAS Triangle Congruence Theorem Similar Polygons Similar Triangles and Proportions AA Triangle Similarity Postulate SAS Triangle Similarity Theorem SSS Triangle Similarity Theorem Altitude of a Triangle Median of a Triangle Concurrency of Medians of a Triangle 30°-60°-90° Triangle Theorem 45°-45°-90° Triangle Theorem Geometric Mean Trigonometric Ratios Inverse Trigonometric Ratios Polygons and Circles Regular Polygon Properties of Parallelograms Rectangle (back to top) Rhombus Square Circle Circles Circle Equation Lines and Circles Tangent Central Angle Measuring Arcs Arc Length Secants and Tangents Inscribed Angle Area of a Sector Inscribed Angle Theorem 1 Inscribed Angle Theorem 2 Inscribed Angle Theorem 3 Segments in a Circle Three-Dimensional Figures Cone Cylinder Polyhedron Similar Solids Theorem Sphere Pyramid Geometry Vocabulary Cards Page 2 Reasoning, Lines, and Transformations (back to top) Geometry Vocabulary Cards Page 3 Basics of Geometry Point – A point has no dimension. P It is a location on a plane. It is point P represented by a dot. Line – A line has one dimension. It is an infinite set of points represented by a line with two arrowheads that extends without end. m A B AB or BA or line m Plane – A plane has two dimensions extending without end. It is often represented by a parallelogram. plane ABC or plane N A B (back to top) Geometry Vocabulary Cards N Page 4 C Basics of Geometry Line segment – A line segment consists of two endpoints and all the points between them. A B AB or BA Ray – A ray has one endpoint and extends without end in one direction. C BC B (back to top) Note: Name the endpoint first. BC and CB are different rays. Geometry Vocabulary Cards Page 5 Geometry Notation Symbols used to represent statements or operations in geometry. BC segment BC BC ray BC BC BC ABC m ABC line BC ABC || (back to top) length of BC angle ABC measure of angle ABC triangle ABC is parallel to is perpendicular to is congruent to is similar to Geometry Vocabulary Cards Page 6 Conditional Statement a logical argument consisting of a set of premises, hypothesis (p), and conclusion (q) hypothesis If an angle is a right angle, then its measure is 90. conclusion Symbolically: if p, then q (back to top) Geometry Vocabulary Cards pq Page 7 Converse formed by interchanging the hypothesis and conclusion of a conditional statement Conditional: If an angle is a right angle, then its measure is 90. Converse: If an angle measures 90, then the angle is a right angle. Symbolically: if q, then p (back to top) Geometry Vocabulary Cards qp Page 8 Inverse formed by negating the hypothesis and conclusion of a conditional statement Conditional: If an angle is a right angle, then its measure is 90. Inverse: If an angle is not a right angle, then its measure is not 90. Symbolically: if ~p, then ~q (back to top) Geometry Vocabulary Cards ~p~q Page 9 Symbolic Representations Conditional if p, then q pq Converse if q, then p qp if not p, Inverse then not q if not q, Contrapositive then not p (back to top) Geometry Vocabulary Cards ~p~q ~q~p Page 10 Deductive Reasoning method using logic to draw conclusions based upon definitions, postulates, and theorems Example: Prove (x ∙ y) ∙ z = (z ∙ y) ∙ x. Step 1: (x ∙ y) ∙ z = z ∙ (x ∙ y), using commutative property of multiplication. Step 2: = z ∙ (y ∙ x), using commutative property of multiplication. Step 3: = (z ∙ y) ∙ x, using associative property of multiplication. (back to top) Geometry Vocabulary Cards Page 11 Inductive Reasoning method of drawing conclusions from a limited set of observations Example: Given a pattern, determine the rule for the pattern. Determine the next number in this sequence 1, 1, 2, 3, 5, 8, 13... (back to top) Geometry Vocabulary Cards Page 12 Proof a justification logically valid and based on initial assumptions, definitions, postulates, and theorems Example: Given: 1 2 Prove: 2 1 Statements 1 2 m1 = m2 m2 = m1 2 1 (back to top) Reasons Given Definition of congruent angles Symmetric Property of Equality Definition of congruent angles Geometry Vocabulary Cards Page 13 Properties of Congruence Reflexive Property For all angles A, A A. An angle is congruent to itself. For any angles A and B, Symmetric Property If A B, then B A . Order of congruence does not matter. For any angles A, B, and C, If A B and B C, then A C. Transitive Property If two angles are both congruent to a third angle, then the first two angles are also congruent. (back to top) Geometry Vocabulary Cards Page 14 Counterexample specific case for which a conjecture is false Example: Conjecture: “The product of any two numbers is odd.” Counterexample: 2 ∙ 3 = 6 One counterexample proves a conjecture false. (back to top) Geometry Vocabulary Cards Page 15 Perpendicular Lines two lines that intersect to form a right angle m n Line m is perpendicular to line n. mn (back to top) Geometry Vocabulary Cards Page 16 Parallel Lines lines that do not intersect and are coplanar m n m||n Line m is parallel to line n. Parallel lines have the same slope. (back to top) Geometry Vocabulary Cards Page 17 Transversal a line that intersects at least two other lines t t a x y b Line t is a transversal. (back to top) Geometry Vocabulary Cards Page 18 Corresponding Angles angles in matching positions when a transversal crosses at least two lines t 1 2 3 4 a 6 5 7 8 b Examples: 1) 2 and 6 2) 3 and 7 (back to top) Geometry Vocabulary Cards Page 19 Alternate Interior Angles angles inside the lines and on opposite sides of the transversal t 1 2 a 3 4 b Examples: 1) 1 and 4 2) 2 and 3 (back to top) Geometry Vocabulary Cards Page 20 Alternate Exterior Angles angles outside the two lines and on opposite sides of the transversal t 1 2 a 3 4 b Examples: 1) 1 and 4 2) 2 and 3 (back to top) Geometry Vocabulary Cards Page 21 Consecutive Interior Angles angles between the two lines and on the same side of the transversal t 1 3 a 2 4 b Examples: 1) 1 and 2 2) 3 and 4 (back to top) Geometry Vocabulary Cards Page 22 Parallel Lines t 2 1 3 a 4 6 5 7 8 b Line a is parallel to line b when Corresponding angles are congruent Alternate interior angles are congruent Alternate exterior angles are congruent Consecutive interior angles are supplementary (back to top) 1 5, 2 6, 3 7, 4 8 3 6 4 5 1 8 2 7 m3+ m5 = 180° m4 + m6 = 180° Geometry Vocabulary Cards Page 23 Midpoint divides a segment into two congruent segments C D M Example: M is the midpoint of CD CM MD CM = MD Segment bisector may be a point, ray, line, line segment, or plane that intersects the segment at its midpoint. (back to top) Geometry Vocabulary Cards Page 24 Midpoint Formula given points A(x1, y1) and B(x2, y2) midpoint M = B (x2, y2) M A (back to top) (x1, y1) Geometry Vocabulary Cards Page 25 Slope Formula ratio of vertical change to horizontal change change in y y2 – y1 slope = m = = change in x x2 – x1 x2 – x 1 B (x2, y2) y2 – y1 A (back to top) (x1, y1) Geometry Vocabulary Cards Page 26 Slopes of Lines Parallel lines have the same slope. Perpendicular lines have slopes whose product is -1. y n p x Vertical lines have undefined slope. Horizontal lines have 0 slope. Example: The slope of line n = -2. The slope of line p = 1 . -2 ∙ 1 = -1, therefore, n p. 2 (back to top) Geometry Vocabulary Cards Page 27 2 Distance Formula given points A (x1, y1) and B (x2, y2) AB x2 x1 2 y 2 y1 x2 – x1 2 B (x2, y2) y2 – y1 A (x1, y1) The distance formula is based on the Pythagorean Theorem. (back to top) Geometry Vocabulary Cards Page 28 Line Symmetry MOM B X (back to top) Geometry Vocabulary Cards Page 29 Point Symmetry Cˊ A P Aˊ C pod S Z (back to top) Geometry Vocabulary Cards Page 30 Rotation y B A C A B C D D x center of rotation Preimage A(-3,0) B(-3,3) C(-1,3) D(-1,0) Image A(0,3) B(3,3) C(3,1) D(0,1) Pre-image has been transformed by a 90 clockwise rotation about the origin. (back to top) Geometry Vocabulary Cards Page 31 Rotation y A A' x center of rotation Pre-image A has been transformed by a 90 clockwise rotation about the point (2, 0) to form image AI. (back to top) Geometry Vocabulary Cards Page 32 Reflection y F F x E D Preimage D(1,-2) E(3,-2) F(3,2) (back to top) D E Image D(-1,-2) E(-3,-2) F(-3,2) Geometry Vocabulary Cards Page 33 Translation y D E C A B x E D C A B Preimage A(1,2) B(3,2) C(4,3) D(3,4) E(1,4) (back to top) Image A(-2,-3) B(0,-3) C(1,-2) D(0,-1) E(-2,-1) Geometry Vocabulary Cards Page 34 Dilation y A A C C B B x Preimage A(0,2) B(2,0) C(0,0) Image A(0,4) B(4,0) C(0,0) F E Preimage E F G H Image E F G H F E H H G P (back to top) Geometry Vocabulary Cards Page 35 G Perpendicular Bisector a segment, ray, line, or plane that is perpendicular to a segment at its midpoint s Z X M Y Example: Line s is perpendicular to XY. M is the midpoint, therefore XM MY. Z lies on line s and is equidistant from X and Y. (back to top) Geometry Vocabulary Cards Page 36 Constructions Traditional constructions involving a compass and straightedge reinforce students’ understanding of geometric concepts. Constructions help students visualize Geometry. There are multiple methods to most geometric constructions. These cards illustrate only one method. Students would benefit from experiences with more than one method and should be able to justify each step of geometric constructions. (back to top) Geometry Vocabulary Cards Page 37 Construct segment CD congruent to segment AB Fig. 1 A B C D Fig. 2 (back to top) Geometry Vocabulary Cards Page 38 Construct a perpendicular bisector of segment AB B A Fig. 1 B A Fig. 2 B A Fig. 3 (back to top) Geometry Vocabulary Cards Page 39 Construct a perpendicular to a line from point P not on the line P P B A B A Fig. 2 Fig. 1 P A P B B A Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 40 Construct a perpendicular to a line from point P on the line A P B A Fig. 1 A Fig. 2 P B A P B Fig. 4 Fig. 3 (back to top) B P Geometry Vocabulary Cards Page 41 Construct a bisector of A A A Fig. 1 A Fig. 2 A Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 42 Construct Y congruent to A A A Y Fig. 1 Y A A Y Y Fig. 2 Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 43 Construct line n parallel to line m through point P not on the line P P m Fig. 1 Draw a line through point P intersecting line m. m Fig. 2 P P n m m Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 44 Construct an equilateral triangle inscribed in a circle Fig. 2 Fig. 1 Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 45 Construct a square inscribed in a circle Fig. 1 Draw a diameter. Fig. 2 Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 46 Construct a regular hexagon inscribed in a circle Fig. 2 Fig. 1 Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 47 Construct the inscribed circle of a triangle Fig. 1 Bisect all angles. Fig. 2 Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 48 Construct the circumscribed circle of a triangle Fig. 2 Fig. 1 Fig. 4 Fig. 3 (back to top) Geometry Vocabulary Cards Page 49 Triangles (back to top) Geometry Vocabulary Cards Page 50 Classifying Triangles Scalene Isosceles Equilateral No congruent sides At least 2 congruent sides 3 congruent sides No congruent angles 2 or 3 congruent angles 3 congruent angles All equilateral triangles are isosceles. (back to top) Geometry Vocabulary Cards Page 51 Classifying Triangles Acute Right Obtuse Equiangular 3 acute angles 1 right angle 1 obtuse angle 3 angles, 1 angle 1 angle each less equals 90 greater than 90 than 90 (back to top) Geometry Vocabulary Cards 3 congruent angles 3 angles, each measures 60 Page 52 Triangle Sum Theorem B A C measures of the interior angles of a triangle = 180 mA + mB + mC = 180 (back to top) Geometry Vocabulary Cards Page 53 Exterior Angle Theorem B 1 A C Exterior angle, m1, is equal to the sum of the measures of the two nonadjacent interior angles. m1 = mB + mC (back to top) Geometry Vocabulary Cards Page 54 Pythagorean Theorem C a B b c hypotenuse A If ABC is a right triangle, then a2 + b2 = c2. Conversely, if a2 + b2 = c2, then ABC is a right triangle. (back to top) Geometry Vocabulary Cards Page 55 Angle and Side Relationships A is the largest angle, therefore BC is the longest side. B A 88o 8 38o 6 54o 12 A 88o 8 54o 38o B (back to top) 6 12 C B is the smallest angle, therefore AC is the shortest side. Geometry Vocabulary Cards Page 56 C Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. B A C Example: AB + BC > AC AC + BC > AB AB + AC > BC (back to top) Geometry Vocabulary Cards Page 57 Congruent Triangles E B F A D C Two possible congruence statements: ABC FED BCA EDF Corresponding Parts of Congruent Figures (back to top) A F AB FE B E BC ED C D CA DF Geometry Vocabulary Cards Page 58 SSS Triangle Congruence Postulate E B A F D C Example: If Side AB FE, Side AC FD, and Side BC ED , then ABC FED. (back to top) Geometry Vocabulary Cards Page 59 SAS Triangle Congruence Postulate B E F C A D Example: If Side AB DE, Angle A D, and Side AC DF , then ABC DEF. (back to top) Geometry Vocabulary Cards Page 60 HL Right Triangle Congruence S R T Y X Z Example: If Hypotenuse RS XY, and Leg ST YZ , then RST XYZ. (back to top) Geometry Vocabulary Cards Page 61 ASA Triangle Congruence Postulate B E F C A D Example: If Angle A D, Side AC DF , and Angle C F then ABC DEF. (back to top) Geometry Vocabulary Cards Page 62 AAS Triangle Congruence Theorem S R T Y Z X Example: If Angle R X, Angle S Y, and Side ST YZ then RST XYZ. (back to top) Geometry Vocabulary Cards Page 63 Similar Polygons C B 4 A F G D 12 2 H 6 E ABCD HGFE Angles A corresponds to H B corresponds to G C corresponds to F D corresponds to E Sides corresponds to corresponds to corresponds to corresponds to Corresponding angles are congruent. Corresponding sides are proportional. (back to top) Geometry Vocabulary Cards Page 64 Similar Polygons and Proportions B 6 C G 4 F x 12 H A Corresponding vertices are listed in the same order. Example: ABC HGF BC = GF 12 6 = x 4 AB HG The perimeters of the polygons are also proportional. (back to top) Geometry Vocabulary Cards Page 65 AA Triangle Similarity Postulate S R Y T Z X Example: If Angle R X and Angle S Y, then RST XYZ. (back to top) Geometry Vocabulary Cards Page 66 SAS Triangle Similarity Theorem B E 14 7 C A 12 F D 6 Example: If A D and AB AC = DF DE then ABC DEF. (back to top) Geometry Vocabulary Cards Page 67 SSS Triangle Similarity Theorem S 13 R 12 Y 6.5 5 T X 2.5 6 Z Example: RT RS ST If = = XZ XY YZ then RST XYZ. (back to top) Geometry Vocabulary Cards Page 68 Altitude of a Triangle a segment from a vertex perpendicular to the opposite side G G A altitudes orthocenter B J B P IH C altitude/height Every triangle has 3 altitudes. The 3 altitudes intersect at a point called the orthocenter. (back to top) Geometry Vocabulary Cards Page 69 Median of a Triangle C median A D B a D is the midpoint of AB; therefore, CD is a median of ABC. Every triangle has 3 medians. (back to top) Geometry Vocabulary Cards Page 70 Concurrency of Medians of a Triangle A centroid D E P C B F Medians of ABC intersect at P and 2 2 2 AP = AF, CP = CE , BP = BD. 3 (back to top) 3 Geometry Vocabulary Cards 3 Page 71 30°-60°-90° Triangle Theorem 60° x 2x x 3 30° 30° x 60° Given: short leg = x Using equilateral triangle, hypotenuse = 2 ∙ x Applying the Pythagorean Theorem, longer leg = x ∙ 3 (back to top) Geometry Vocabulary Cards Page 72 45°-45°-90° Triangle Theorem 45° x 2 x 45° x Given: leg = x, then applying the Pythagorean Theorem; hypotenuse2 = x2 + x2 hypotenuse = x 2 (back to top) Geometry Vocabulary Cards Page 73 Geometric Mean of two positive numbers a and b is the positive number x that satisfies a x = . x b x2 = ab and x = ab . In a right triangle, the length of the altitude is the geometric mean of the lengths of the two segments. A x B 9 4 C Example: = , so x2 = 36 and x = 36 = 6. (back to top) Geometry Vocabulary Cards Page 74 Trigonometric Ratios B (hypotenuse) c a (side opposite A) A b (side adjacent A) C sin A = side opposite A = a c hypotenuse cos A = side adjacent A = b c hypotenuse tan A = side opposite A = a side adjacent to A b (back to top) Geometry Vocabulary Cards Page 75 Inverse Trigonometric Ratios B A c a b C Definition Example If tan A = x, then tan-1 x = mA. tan-1 a = mA b If sin A = y, then sin-1 y = mA. sin-1 a = mA c If cos A = z, then cos-1 z = mA. cos-1 b = mA c (back to top) Geometry Vocabulary Cards Page 76 Polygons and Circles (back to top) Geometry Vocabulary Cards Page 77 Regular Polygon a convex polygon that is both equiangular and equilateral Equilateral Triangle Each angle measures 60o. Square Each angle measures 90o. Regular Pentagon Each angle measures 108o. Regular Hexagon Each angle measures 120o. Regular Octagon Each angle measures 135o. (back to top) Geometry Vocabulary Cards Page 78 Properties of Parallelograms Opposite sides are parallel and congruent. Opposite angles are congruent. Consecutive angles are supplementary. The diagonals bisect each other. (back to top) Geometry Vocabulary Cards Page 79 Rectangle A rectangle is a parallelogram with four right angles. Diagonals are congruent. Diagonals bisect each other. (back to top) Geometry Vocabulary Cards Page 80 Rhombus A rhombus is a parallelogram with four congruent sides. Diagonals are perpendicular. Each diagonal bisects a pair of opposite angles. (back to top) Geometry Vocabulary Cards Page 81 Square A square is a parallelogram and a rectangle with four congruent sides. Diagonals are perpendicular. Every square is a rhombus. (back to top) Geometry Vocabulary Cards Page 82 Circle all points in a plane equidistant from a given point called the center Point O is the center. MN passes through the center O and therefore, MN is a diameter. OP, OM, and ON are radii and OP OM ON. RS and MN are chords. (back to top) Geometry Vocabulary Cards Page 83 Circles A polygon is an inscribed polygon if all of its vertices lie on a circle. A circle is considered “inscribed” if it is tangent to each side of the polygon. (back to top) Geometry Vocabulary Cards Page 84 Circle Equation y (x,y) r y x x x2 + y2 = r2 circle with radius r and center at the origin standard equation of a circle (x – h)2 + (y – k)2 = r2 with center (h,k) and radius r (back to top) Geometry Vocabulary Cards Page 85 Lines and Circles C A D B Secant (AB) – a line that intersects a circle in two points. Tangent (CD) – a line (or ray or segment) that intersects a circle in exactly one point, the point of tangency, D. (back to top) Geometry Vocabulary Cards Page 86 Tangent Q S R A line is tangent to a circle if and only if the line is perpendicular to a radius drawn to the point of tangency. QS is tangent to circle R at point Q. Radius RQ QS (back to top) Geometry Vocabulary Cards Page 87 Tangent C A B If two segments from the same exterior point are tangent to a circle, then they are congruent. AB and AC are tangent to the circle at points B and C. Therefore, AB AC and AC = AB. (back to top) Geometry Vocabulary Cards Page 88 Central Angle an angle whose vertex is the center of the circle B minor arc AB D C major arc ADB A ACB is a central angle of circle C. Minor arc – corresponding central angle is less than 180° Major arc – corresponding central angle is greater than 180° (back to top) Geometry Vocabulary Cards Page 89 Measuring Arcs B C 70° 110° R D A Minor arcs Major arcs Semicircles The measure of the entire circle is 360o. The measure of a minor arc is equal to its central angle. The measure of a major arc is the difference between 360° and the measure of the related minor arc. (back to top) Geometry Vocabulary Cards Page 90 Arc Length B 4 cm 120° C A Example: (back to top) Geometry Vocabulary Cards Page 91 Tangents Two tangents x° 1 y° m1 = (back to top) 1 (x°- y°) 2 Geometry Vocabulary Cards Page 92 Inscribed Angle angle whose vertex is a point on the circle and whose sides contain chords of the circle B A C (back to top) Geometry Vocabulary Cards Page 93 Area of a Sector region bounded by two radii and their intercepted arc Example: cm (back to top) Geometry Vocabulary Cards Page 94 Inscribed Angle Theorem D B A C If two inscribed angles of a circle intercept the same arc, then the angles are congruent. BDC BAC (back to top) Geometry Vocabulary Cards Page 95 Inscribed Angle Theorem B A O C mBAC = 90° if and only if BC is a diameter of the circle. (back to top) Geometry Vocabulary Cards Page 96 Inscribed Angle Theorem T 92 95 H J 85 A 88 M M, A, T, and H lie on circle J if and only if mA + mH = 180° and mT + mM = 180°. (back to top) Geometry Vocabulary Cards Page 97 Segments in a Circle c b a d If two chords intersect in a circle, then a∙b = c∙d. Example: 12(6) = 9x 72 = 9x 8=x (back to top) x 12 Geometry Vocabulary Cards 6 9 Page 98 Three-Dimensional Figures (back to top) Geometry Vocabulary Cards Page 99 Cone solid that has a circular base, an apex, and a lateral surface apex lateral surface (curved surface of cone) slant height (l) height (h) radius(r) base 1 2 V = r h 3 L.A. (lateral surface area) = rl S.A. (surface area) = r2 + rl (back to top) Geometry Vocabulary Cards Page 100 Cylinder solid figure with congruent circular bases that lie in parallel planes base height (h) base radius (r) V = r2h L.A. (lateral surface area) = 2rh S.A. (surface area) = 2r2 + 2rh (back to top) Geometry Vocabulary Cards Page 101 Polyhedron solid that is bounded by polygons, called faces (back to top) Geometry Vocabulary Cards Page 102 Similar Solids Theorem If two similar solids have a scale factor of a:b, then their corresponding surface areas have a ratio of a2: b2, and their corresponding volumes have a ratio of a3: b3. cylinder A cylinder B Example A (back to top) B scale factor a:b 3:2 ratio of surface areas a2: b2 9:4 ratio of volumes a3: b3 27:8 Geometry Vocabulary Cards Page 103 Sphere a three-dimensional surface of which all points are equidistant from a fixed point radius 4 3 V = r 3 S.A. (surface area) = 4r2 (back to top) Geometry Vocabulary Cards Page 104 Pyramid polyhedron with a polygonal base and triangular faces meeting in a common vertex vertex slant height (l) height (h) area of base (B) base perimeter of base (p) 1 V = Bh 3 1 L.A. (lateral surface area) = lp 2 1 S.A. (surface area) = lp + B 2 (back to top) Geometry Vocabulary Cards Page 105