Glossary of dictionary terms in the AP geometry units

Transcription

1 Glossary of dictionary terms in the AP geometry units affine linear equation: an equation in which both sides are sums of terms that are either a number times y or a number times x or just a number [SlL2-D5] angle bisector: a segment that divides an angle into two equal parts [Cir1-5] Angle-Side-Angle Theorem, or A-S-A: the statement expressing that two triangles are congruent if two corresponding pairs of angles and the side between them are the same, respectively [SSC4-D1] arc of a circle: segment of a circle [Cir4-0], see also circle arrow diagram: a scheme, a drawing, or a table that summarizes the effect of one or more geometric transformations on certain geometric figures by indicating the initial and the final objects of the transformation [SSC2-D1b] axes: plural for axis [LAP1-D1] axis: either the horizontal or the vertical lines, marked by numbers, and helping to locate a spot in a rectangular coordinate system [LAP1-D1] center of circle: see circle central angle: an angle with vertex at the center of a circle [Cir4-0], see circle centroid: the intersection of the 3 medians in a triangle [TPh3-4] chord: segment with endpoints on a circle [Cir1-0], see also circle circle: a figure in a plane with the property that all its points are equally distanced from a fix point (called the center of the circle) [SSC2-D1a]

2 Center of circle Circle Circumference = distance around the circle Chord = segment with endpoints on the circle Tangent line (see Cir1-4) Point of tangency = point where the tangent line touches the circle Diameter = chord containing center Radius = segment from center to circle [Cir1-0] Arc l Sector (area) Central angle Inscribed angle or angle subtending arc l Radius R Center O [Cir4-0] circumcircle: the circle that contains all the vertices of a triangle. Also, this circle is the circle circumscribed about the triangle, and the center of the circle is called the circumcenter of the triangle, and the triangle is said to be inscribed in the circle. [Cir1-3] circumference: distance around the circle [Cir1-0], see circle

3 circumscribes the circle: every side is tangent to the circle [Cir1-6; Cir2-3] collinear: not all on the same line [Cir1-3] concentric: with the same center [Cir5-4] congruent: the property of two geometric figures so that there is an isometry that takes one onto the other and they match perfectly [SSC4-D1; HCh1-D2; HCh1-D2] conversely: a mathematical term implying an alternative way of looking at a mathematical statement [SlL4-D1] convex: polygon with all interior angles less than 180 [TPh2-10] coordinate system: a procedure of assigning to each point in a certain region a collection of (2 or more) numbers and letters (or words) that determines its position [CSy-1] coordinates: the collection of numbers and letters assigned to a point in a coordinate system [CSy-1] cos( ): the x-coordinate of the point on the unit circle with central angle ( ). [Cir5- D3] cross-section of a solid: the intersection of the solid with a plane [TPh3-3] cube: a polyhedron made up of 6 squares with 3 squares coming together at each vertex [TPh2-4] diameter: chord with endpoints on the circle [Cir1-0] definition of a shape: a description that is sufficient to decide whether a figure is or it is not of that shape [SSC1.2] degenerate (equation): an equation that either has no solutions (that is, it is impossible to solve ) or it has an infinity of solutions (that is, it is an identity) [SlL2-D6] diagonal: a line segment in the interior of a polygon joining two vertices [LAP2-D3]; [Cir2-D1] displacement (from a point A to a point B): the directed segment that starts at A and ends at B [HCh4-D2] dodecahedron: a regular polyhedron made up of 12 pentagons with 3 pentagons coming together at each vertex [TPh2-2]

4 end points of the line segment: the two extremities of a line segment [HCh1-D2] equation of a line: the algebraic expression holding together the two coordinates of all points of a given line, and none others [SlL2-D2] equidistant: two lines that stay the same distance apart (also see parallel ) [LAP1- D2; SlL1-D1] exterior angle: the supplementary angle of an angle of a polygon [TPh2-10], [Cir4-2] Exterior Angle Theorem: On the plane, any exterior angle is the sum of the opposite interior angles, and. ( = + ) [Cir4-2] extrinsic: a point-of-view from the outside [NEG1-D2] general position: a geometric figure with no particular characteristics (for instance, a rectangle with sides not parallel/perpendicular to other sides) [IGA1] geodesics (geo-dees-iks): paths that are intrinsically straight on a sphere (or other surfaces) [NEG1-4] glide symmetry: the geometric property of a figure that can be moved successively in a direction with perfect self-preservation [SSC2-D1a] great circles: the biggest circles on the sphere (the ones that divide the sphere in half) [NEG1-D2] half-turn symmetry: a rotation through half of a full revolution about a point; it is the geometric property of a figure for which half of it lies exactly to the opposite of a certain point [SSC2] hypotenuse: the side opposite to the right angle in a right angle triangle [LAP3-D1] icosahedron: a regular polyhedron made up of 20 triangles with 5 triangles coming together at each vertex [TPh2-1] identity: a symmetry that leaves a geometric figure unchanged [SSC3-D1] incenter: the center of the inscribed circle [Cir1-D1] infinite slope: the slope of a vertical line [SlL1-D1] inscribed angle: an angle inside a circle with vertex on the circle [Cir4-0], see also circle

5 inscribed circle: the circle that is tangent to all three sides of a triangle, its center is called the incenter of the triangle. [Cir1-6] inscribed in the circle: all vertices on the circle [Cir1-3], [Cir2-3] inscribed in the triangle: a circle that lies inside the triangle and touches all three sides at one point, respectively [TPh3-D1] intrinsic: a point-of-view from the inside [NEG1-D2] isometry (i-som-e-tree): a transformation that preserves distances and angle measures [SSC2-D1a] Law of Cosines: If we know two sides a and b and the included angle, then the third side c satisfies: c 2 = b 2 + a 2 2(ba) cos( ). [Cir5-6] line segment: a part of a line that joins two points [HCh1-D2] location vector (of a point): a vector starting in a conventional origin and pointing to a given end-point [HCh4-D2] median: the segment in a triangle (or on a face of a tetrahedron) from a vertex to the midpoint of the opposite side (or edge) [TPh3-2] n-gon: a polygon with n sides [TPh2-10] numbers: the arithmetic value on the real line that designates the location of a point [GRL1-D2] octahedron: a regular polyhedron made up of 8 triangles with 4 triangles coming together at each vertex [TPh2-3; TPh3-6] order of a symmetry group: the number of distinct symmetries of a symmetry group, excluding the identity [SSC3-D1] ordering: arranging certain measures (numbers or line segments from the smallest to the greatest [HCh1-D5] parallel: two lines that stay the same distance apart no matter how far they are extended (also see equidistant ) [LAP1-D2; SlL1-D1] perpendicular bisector of a line segment: the line that intersects the segment at its midpoint and is perpendicular to the segment. [Cir1-2] perpendicular curves: two curves are perpendicular at a point P if the tangent lines at P are perpendicular to each other. [Cir1-D1]

6 pi ( ): the ratio of the circumference to the diameter of any circle in a plane [Cir2-D1] perimeter: the distance around a polygon [Cir2-D1] point (or location): the simple geometric entity, with no parts [HCh4-D2] point of tangency: point where the tangent line touches the circle [Cir1-0], see also circle polar coordinates: The point with polar coordinates [R, ] is the point with rectangular coordinates ( R cos( ), R sin( ) ). P = ( R cos( ), R sin( ) ) R 0 [Cir5-4] polygon: a closed figure in the plane with straight edges. polyhedron: a solid in 3-space with each of whose faces is a polygon. Platonic solid: same as regular polyhedron [TPh2-D1] product (of symmetries): the result of two or more successive symmetries [SSC3-D1] proof: a communication that convinces and answers why? [SSC2-D1b] radian measure (of a central angle ): the ratio of the arc and the radius [Cir4-1], [Cir5-2] radius: a segment from center to circle, see also circle [Cir1-0] ratio: the proportion (the result of the division) between the lengths of two segments [ScM1-D2] real line: the integer number line, with all points in between integers added [GRL1-D2] reciprocal (of a number m): the proportion between 1 and the given number m; that is, the reciprocal is 1/m [SlL1-8] rectangular coordinate system: the horizontal and vertical axes, taken together in order to locate a point in the plain [LAP1-D1]

7 rectangular coordinates: pairs of numbers, the first on the horizontal axis and the second on the vertical axis; each pair uniquely determines the planar position of a spot [LAP1-D1] reflection (or mirror) symmetry: the geometric property of a figure that can be folded along a straight line so that its two halves perfectly overlap after folding [SSC2] regular polyhedron: a polyhedron with all the faces are the same regular polygon [TPh2-D1] regular polygon: a polygon with all equal sides and equal interior angles [TPh2-D1] sector of a circle: area bounded by an arc and central angle of a circle [Cir4-0], see also circle Side-Angle-Side Theorem, or S-A-S: the statement expressing that two triangles are congruent if two corresponding pairs of sides and the angle between them are the same, respectively [SSC4-D1] Side-Side-Side Theorem, or S-S-S: the statement expressing that two triangles are congruent if all three corresponding pairs of sides are of the same length [SSC4-D1; SSC5-D1] sin( ): the y-coordinate of the point on the unit circle with central angle ( ). [Cir5- D3] skew lines: lines which are not parallel and do not intersect, even if extended [TPh3-2] slope (of a line or line segment): the proportion of the change in the y-coordinates to the change in the x-coordinates when we consider a movement between two points [SlL1-D1] slope-intercept form of the equation of a line : the equation of a line written as y = mx + b, where m is the slope of the line and b is the y-intercept [SlL2-D4] smooth curve: a curve that has a tangent line at every point [Cir3-D2] solving a system of simultaneous equations: finding the pairs of coordinates that simultaneously verify two (or more) equations [SlL3-D1] space-filling curve: a curve that has non-zero area [Cir3-D2] straight line: a line that has translation symmetry, half-turn symmetry and reflection symmetry [SSC2-D1a]

8 subtending an arc: an inscribed angle intersecting the endpoints of the arc [Cir4-0], see also circle symmetry group: all the distinct symmetries of a geometric figure, considered together but without repetition [SSC3-D1] symmetry of a figure: an isometry of a region of space that takes the figure (or the portion of it in the region) onto itself [SSC2-D1a] tangent line to a curve at the point at the point P: when you zoom-in on P, the curve and the line become indistinguishable. [Cir1-D1] tangent function, tan( ): sin( )/cos( ). [Cir5-7] tetrahedron: a regular polyhedron made up of 4 triangles with 3 triangles coming together at each vertex [TPh2-5] theorem: a statement for which we have a proof [SSC2-D1b] tiling: a covering of the plane with a geometric form repeated ad infinitum so that there are no gaps and no overlaps between the adjacent figures [TPh1-1] triangle inequality: an algebraic relationship expressing that in any triangle the sum of two sides must be longer than the third side [SSC5-D1] unit circle: a circle for which the unit of length measure is the radius [Cir5-D2] vector: an oriented line segment, having magnitude (length) and direction (from one designated end to the other) [HCh4-D2] vertices: the points that lie at the corners of a planar or spatial geometric figure [LAP2- D3] width (of a polyhedron): distance between two parallel planes arranged so that both touch the tetrahedron [TPh3-1]; [Cir2-D2] y-intercept: the value of y at which a line intersects the y-axis [SlL2-D4]