Geometry Vocabulary. Name Class

Transcription

1 Geometry Vocabulary Name Class Definition/Description Symbol/Sketch 1 point An exact location in space. In two dimensions, an ordered pair specifies a point in a coordinate plane: (x,y) 2 line 3a line segment written and read: point A Note: capital letter is used An infinite set of points forming a straight path extending indefinitely in two directions.!## " written: AB read: line AB Note: the drawing of a line has visible points while the symbol does not Note: named using any 2 points on the line A part of a line between two endpoints. 3b measurement of a line segment written: AB read: line segment AB Note: the letters indicate the points at the beginning and the end of the line segment Note: the drawing of a line segment has visible points while the symbol does not The length of a line segment. written: AB ex.: AB = 5cm read: measurement of line segment AB 4 endpoint Either of two points that mark the ends of a line segment.

2 5 ray A portion of a line that has one endpoint and extends forever in one direction.!!! " written: AB read: ray AB Notes on symbol: the arrow on top of the symbol always points right; it is always 2 letters; first letter is always the endpoint Note: the drawing of a ray has a visible point while the symbol does not 6 intersecting lines Two lines that cross. 7 parallel lines Two straight lines on a two-dimensional surface that never intersect and are the same distance apart. symbol:!! ex. AB ##"!##" $ CD read: is parallel to Note: the drawing of parallel lines has different symbols (arrow heads on lines) to indicate parallel 8 perpendicular lines 9 vertex (plural: vertices) Lines, segments or rays that intersect to form right angles.!## "!##" symbol: ex. AB CD read: is perpendicular to Note: the drawing of perpendicular lines has a different symbol to indicate perpendicular (lines forming small square at intersection) The point at which two rays, line segments or lines meet. Note: no points drawn (exaggerated) at vertices 10 non-linear (adjective) Describes a set of points that do not lie on a straight line when connected. Compare to linear: a set of points that do lie on a straight line when connected

3 11 plane A flat surface that extends indefinitely in all directions. It has no thickness. 12 skew lines Lines that lie in different planes that are neither parallel nor intersecting. 13 parallel planes Planes that do not intersect. 14 perpendicular planes Planes that intersect to form right angles. 15a 15b angle measurement of an angle A geometric figure made up of two rays or line segments that have the same endpoint. written:!abc(or ABC) or!b(or B) read: angle ABC or angle B Note: Usually three letters are used to name an angle. One can be used if the angle can not be mistaken for any other angle. The amount an angle is open. The most common units used for measuring angles are degrees and radians. (See Definition #23.) written: m ABC(or m!abc) read: the measure(or measurement) of angle ABC example: m ABC = 45

4 16 vertical angles A pair of opposite, congruent angles formed by intersecting lines. 17 adjacent angles Angles that share a common side and vertex but no common interior points 18 acute angle An angle with a measure greater than 0 and less than right angle An angle whose measure is obtuse angle An angle greater than straight angle An angle whose measure is protractor A tool used to draw or measure angles.

5 23 degree 1 Represents of a full rotation of a 360 circle, usually denoted by the symbol:. Degrees are used for measuring (plane) angles and arcs. Note: A degree is not an International System of Units (SI) unit, as the SI unit for angles is radian, but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2π radians, one degree is equivalent to π radians complementary angles Two angles whose measures add to b supplementary angles Two angles whose measures add to linear pair Two adjacent, supplementary angles. Together their non-shared sides (or rays) will form a straight angle. 26 polygon A two-dimensional closed figure made of straight line segments (sides or edges) connected end to end (at vertices). 27 triangle A polygon with three sides.

6 28 Triangle Sum Theorem The theorem that states: the measures of the angles in a triangle add to congruent Figures, segments, or angles that are the same size and same shape. Symbol: read: is congruent to Note: In a diagram, the same number of tick marks indicate that sides (or angles) are congruent. 30 equilateral triangle A triangle with all sides equal. 31 isosceles triangle A triangle with two sides of equal length. 32 scalene triangle A triangle with no two sides of equal length. 33 acute triangle A triangle in which all three angles are acute (less than 90 ). 34 obtuse triangle A triangle with an obtuse angle.

7 35 right triangle A triangle with one right angle in it. 36 hypotenuse In a right triangle, the longest side of the triangle, opposite the right angle. 37 leg Either of two shorter sides of a right triangle. 38 Pythagorean Theorem For right triangles: leg 2 + leg 2 = hypotenuse 2 Uses: to find the length of any third side of a right triangle when other two are known to see if a given triangle is a right triangle 39 compass A tool used to create a circle. 40 midpoint The middle point of a line segment. 41 bisect Divide (a line, angle shape, etc.) into two equal parts.

8 42 angle bisector A ray that divides an angle into two congruent parts. 43 perpendicular bisector A line, segment or ray that divides a segment into two congruent segments and is perpendicular to the segment. 44 proportion An equation of two equivalent ratios. 45 corresponding parts Points, edges (sides), or angles in congruent or similar figures that are arranged in similar ways. 46 similar Figures that have the same shape but not necessarily the same size. The lengths of the corresponding sides are proportional to one another; the corresponding angles are congruent. symbol is written: symbol is read: is similar to Note: congruent figures are (a special type of) similar with a scale factor of scale factor A ratio between two sets of measurements. scale factor = side ratio 48 circle The set of all points in two dimensions that are the same distance r from a fixed point P. The fixed point P is called the center of the circle and the distance r is called the radius.

9 49 center (of a circle) The point equidistant from all points on a circle. 50 radius (plural: radii) The distance from the center to a point on a circle. 51 chord A line segment that connects two points on a circle. Note: the endpoints of the chord are on the circle. 52 diameter A chord (or line segment that has its endpoints on the circle) that passes through the center. 53 circumference The distance around the outside of a circle. C = πd or C = 2πr (d=diameter, r=radius) 54 ratio A comparison of two numbers or quantities. They are measured in the same or similar units. 55 rate A ratio that compares two quantities measured in different types of units.

10 56 pi (π) The ratio of the circumference of a circle to the length of its diameter. π = C d! 3.14 or formula An equation that shows a mathematical relationship. 58 area The measure in square units of the interior region of a plane figure or the surface of a three-dimensional figure. 59 square unit A square whose sides measure 1 unit in length. Area is measured in square units. 60 area of a circle A = πr 2 written: sq. units or units 2 example: sq. cm or cm 2 (r = radius) 61 arc The portion of a circle between two points on a circle. Arcs can be major (longer than a semicircle) or minor. written: AB! read: arc AB (minor arc) Note: minor arcs are named using 2 points Note: major arcs (including semicircles) are named using 3 points Note: Arcs have the same measure as their central angle. (See definition #63)

11 62 semicircle An arc that represents half of a circle. written: ABC! read: semicircle ABC Notes: 3 points are needed to name semicircles; A and C are the endpoints of this semicircle Note: major arcs are named like semicircles 63 central angle An angle whose vertex is the center of a circle. 64 sector A part of the interior of a circle bounded by two radii and the arc between their endpoints. Note: looks like a piece/slice of pie 65 regular polygon A polygon in which all sides are congruent and all angles are congruent. 66 quadrilateral A polygon with four sides. (some special quadrilaterals: squares, rectangles, trapezoids, parallelograms, rhombuses or rhombi) 67 pentagon A polygon with five sides. 68 hexagon A polygon with six sides.

12 69 heptagon A seven sided polygon. 70 octagon A polygon with eight sides. 71 nonagon A polygon with nine sides. 72 decagon A ten sided polygon. 73 undecagon or hendecagon An eleven sided polygon. 74 dodecagon A twelve sided polygon. 75a trapezoid A quadrilateral with exactly one pair of parallel sides. (definition under debate) Some special trapezoids are isosceles trapezoids and right trapezoids. See below.

13 75b isosceles trapezoid A trapezoid whose non-parallel sides are congruent. 75c right trapezoid A trapezoid with a right angle. 76 parallelogram A quadrilateral with both pairs of opposite sides parallel. 77 rectangle A quadrilateral with four right angles. (Its two pairs of opposite sides are parallel and congruent.) 78 square A quadrilateral with four congruent sides and four right angles. Note: squares must be rhombi (or rhombuses) and rectangles. 79 rhombus A quadrilateral with four congruent sides. 80 kite A quadrilateral with two pairs of adjacent, congruent sides.

14 81 diagonal A diagonal connects two vertices of a polygon but is not a side. 82 height The perpendicular distance between two bases, or between a vertex and a base. 83 base (of a 2-D figure) For a triangle, the base may be any side, although it is usually the bottom one. For a trapezoid, the two parallel sides are the bases. 84 perimeter The distance around a figure on a flat surface. 85 perimeter of rectangle P= 2l + 2w or P= 2b+2h (l= length, w=width, b=base, h=height) 86 area of a rectangle and/or parallelogram A = bh (b = base, h = height) 87 perimeter of a square P= 4s (s=side length)

15 88 area of a square A = s 2 (s = side) 89 altitude of a triangle Height. The perpendicular distance from a vertex to the opposite side (or its extension) of a triangle. 90 area of a triangle A = 1 2 bh (b = base, h = height) 91 area of a trapezoid A = 1 h(top + bottom bases) 2 (h = height) or A= average of bases height 92 composite figure A figure made up of simple geometric shapes (rectangles, circles, etc.). 93 polyhedron A three-dimensional figure with no holes in which all faces are polygons. 94 face A flat side of a polyhedron.

16 95 edge The line segment where two faces of a solid figure meet. 96 pyramid A polyhedron with a polygonal base and whose other faces are triangles with a common vertex. A pyramid is named for the shape of its base. Note: v + f = e tetrahedron A polyhedron with four faces. Also known as a triangular pyramid 98a prism A polyhedron with and two parallel, congruent bases. The remaining faces are parallelograms. No holes are permitted in the solid. A prism is named for the shape of its base. Note: Prisms can be right or oblique. 98b right prism A prism in which the joining edges and faces are perpendicular to the base faces. This applies if the joining faces are rectangular. 98c oblique prism A prism in which the joining edges and faces are not perpendicular to the base faces. The joining faces are not rectangular. 99 cube A rectangular prism with 6 congruent faces, all squares.

17 100 cylinder Commonly, a three dimensional object with two circular, congruent and parallel bases. (A soda can.) Note: Cylinders can be oblique (slanted). 101 cone A three-dimensional figure with one circular base and one vertex. Note: Cones can be oblique. 102 sphere A round 3-D figure. Looks like a ball. 103 hemisphere Half of a sphere. 104 base (of a 3-D figure) 105 lateral face (of a prism) For a cylinder or a prism, either one of the two congruent parallel faces may be the base. For a pyramid or cone, the base is the (flat) face that does not contain the vertex (where all the sides come together). Parallelograms that connect the bases. 106 lateral area (of a prism) The sum of the areas of the lateral faces.

18 107 lateral surface (of a cylinder) The curved surface that connects the bases. 108 surface area The total area of all faces and bases of a polyhedron, cylinder, cone or pyramid. 109 net A two dimensional one-piece plan which can be folded into a three dimensional shape. 110 volume The number of cubic units inside a three dimensional object. 111 cubic unit A cube whose edges measure 1 unit in length. Volume is measured in cubic units. written: cu. units or units surface area of a prism example: cu. cm or cm 3 SA = 2B + L or SA = 2B + Ph (B=base area, L= lateral area, P=perimeter, h=height) 113 surface area of a cylinder SA = 2πr 2 + 2πrh or SA = 2πr 2 + πdh (r=radius, d=diameter, h=height)

19 114 volume of a prism V = Bh (B=base area, h=height) 115 volume of a cylinder V = πr 2 h (r=radius, h=height) 116 volume of a pyramid V = 1 3 Bh (B=base area, h=height) 117 volume of a cone V = 1 3 πr 2 h (r=radius, h=height) 118 slant height (of a pyramid or cone) The distance from the base to its vertex, measured along the lateral surface. 119 surface area of a cone SA = πrs + πr 2 (r=radius, s=slant height) 120 transversal A line that intersects a system of lines.

20 121 corresponding angles The angles that occupy the same relative position at each intersection when two lines are intersected by a transversal. If the two lines are parallel, the corresponding angles are congruent. 122 interior angles 1) The angles located in the interior of a polygon. 2) The angles located between the nontransversal lines when the lines are cut by a transversal. 123 exterior angles 1) The outer angles formed by the side of polygon and the adjacent side extended outward. 2) The angles not located between the non-transversal lines when the lines are cut by a transversal. 124 alternate angles Angles on opposite sides of a transversal. Can be alternate interior angles (aka Z angles ) or alternate exterior angles. 125 transformation A change in the size or position of a figure. 126 image A figure resulting from a transformation. 127 translation (a.k.a slide) A transformation resulting in the movement(slide) of a figure along a straight line.

21 128 dilation A transformation in which a figure is enlarged or reduced by a given scale factor around a given center point, called the center of dilation. 129 center of dilation A fixed point in the plane about which all points are expanded or contracted. 130 rotation A transformation in which a figure is rotated or turned around a point. 131 reflection A transformation of a figure that flips (or reflects) the figure across a line. 132 line of reflection A line that a figure is flipped across to create a mirror image of the original figure. 133 symmetry Here are two types (not the only two): bilateral symmetry: half object is mirror image of other half radial symmetry: new image is an identical rotation of original figure Note: the opposite of symmetry is asymmetry. 134 line of symmetry (a.k.a. axis of symmetry) A line that runs down the center of a shape such that if the shape were folded in half on this line, the two halves would match up perfectly. The two halves would be mirror images of one another.

22 135 construction Various geometric objects created using only a compass and a straightedge. 136 cross section or slice the intersection of a body in 3- dimensional space with a plane (or of a body in 2-dimensional space with a line)

23 18 acute angle 33 acute triangle 17 adjacent angles 124 alternate angles 89 altitude of a triangle Index 24 complementary angles 92 composite figure 101 cone 29 congruent 135 constructions 103 hemisphere 73 hendecagon 69 heptagon 68 hexagon 36 hypotenuse 15a angle 121 corresponding angles 126 image 42 angle bisector 61 arc 45 corresponding parts 136 cross section 122 interior angles 6 intersecting lines 58 area 99 cube 75b isosceles trapezoid 60 area of a circle 86 area of a rectangle and/or parallelogram 88 area of a square 91 area of a trapezoid 90 area of a triangle 83 base (2-D) 104 base (3-D) 41 bisect 49 center (of a circle) 129 center of dilation 63 central angle 51 chord 48 circle 53 circumference 39 compass 111 cubic unit 100 cylinder 72 decagon 23 degree 81 diagonal 52 diameter 128 dilation 74 dodecagon 95 edge 4 endpoint 30 equilateral triangle 123 exterior angles 94 face 57 formula 82 height 31 isosceles triangle 80 kite 106 lateral area (of a prism) 105 lateral face (of a prism) 107 lateral surface (of a cylinder) 37 leg 2 line 25 linear pair 132 line of reflection 134 line of symmetry (a.k.a. axis of symmetry) 3a line segment 15b measurement of an angle 3b measurement of a line segment 40 midpoint 109 net

24 10 non-linear 71 nonagon 38 Pythagorean Theorem 66 quadrilateral 78 square 59 square unit 98c oblique prism 23 radian 21 straight angle 20 obtuse angle 50 radius 24b supplementary angles 34 obtuse triangle 70 octagon 7 parallel lines 13 parallel planes 75 parallelogram 67 pentagon 84 perimeter 87 perimeter of a square 85 perimeter of rectangle 43 perpendicular bisector 8 perpendicular lines 14 perpendicular planes 56 pi (π) 11 plane 1 point 26 polygon 93 polyhedron 98a prism 44 proportion 22 protractor 96 pyramid 55 rate 54 ratio 5 ray 77 rectangle 131 reflection 65 regular polygon 79 rhombus 19 right angle 98b 75c right prism right trapezoid 35 right triangle 130 rotation 47 scale factor 32 scalene triangle 64 sector 62 semicircle 46 similar 12 skew lines 118 slant height (of a pyramid or cone) 136 slice 102 sphere 108 surface area 119 surface area of a cone 113 surface area of a cylinder 112 surface area of a prism 133 symmetry 97 tetrahedron 125 transformation 127 translation (a.k.a slide) 120 transversal 75a trapezoid 27 triangle 28 Triangle Sum Theorem 73 undecagon 9 vertex (plural: vertices) 16 vertical angles 110 volume 117 volume of a cone 115 volume of a cylinder 114 volume of a prism 116 volume of a pyramid

25