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Geometry Dictionary

Geometry Dictionary. Sasha Vasserman. AA Theorem of Similarity . Two triangles are similar if two pairs of corresponding angles are congruent. AAS Theorem of Congruence.

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Geometry Dictionary

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  1. Geometry Dictionary Sasha Vasserman

  2. AA Theorem of Similarity • Two triangles are similar if two pairs of corresponding angles are congruent

  3. AAS Theorem of Congruence • Two triangles are congruent if two pairs of corresponding angles are congruent and a non-included pair of corresponding sides are congruent

  4. Abscissa • The x-coordinate of a point in the coordinate plane

  5. Absolute value • For a number x, denoted by |x |, its distance from 0 on the number line. Thus, |x| always represents a nonnegative number

  6. Acute angle • An angle whose degree measure is < 0 and > 90

  7. Acute traingle • A triangle with three acute angles

  8. Adjacent angles • Two angles that have the same vertex and share one side, but do not have any inferior points in common

  9. Alternate interior angles • Pairs of angles formed when a transversal intersects two lines. The two angles ion each pair are between the two lines, have different vertices, and lie on opposite sides of the transversal

  10. Altitude • A segment that is perpendicular to the side of the figure to which it is drawn

  11. Angle • The union of two rays that have the same end point

  12. Angle bisector • A line or any part of a line that contains the vertex of an angle and that divides the angle into two congruent angles. An angle has exactly one angle bisector

  13. Angle of depression • An angle formed by a horizontal ray of sight and the ray that is the line of sight to an object below the horizontal ray

  14. Angle of elevation • An angle formed by a horizontal ray of sight and the ray that is the line of sight to an object above the horizontal ray

  15. Apothem • For a regular polygon, the radius of its inscribed circle

  16. Arc of a chord • The minor arc of a circle whose end points are the end points of a chord. If the chord is a diameter, then either semicircle is an arc of the diameter

  17. Area • For a plane geometric figure, the number of square units it contains

  18. ASA Theorem of Congruence • Two triangles are congruent if two pairs of corresponding angles are congruent and the sides included by these angles are congruent

  19. Base angles of an isosceles triangle • The congruent angles that lie opposite the congruent sides of an isosceles triangle

  20. Base of an isosceles triangle • The non-congruent side of the isosceles triangle

  21. Base of a trapezoid • The parallel sides of a trapezoid

  22. Betweenness of points • A term that refers to the order of three collinear points. If A, B, and C are three different collinear points, point C us between points A and b if AC + CB = AB

  23. Bisect • To divide into two equal parts

  24. Center of a regular polygon • The common center of the circles inscribed and circumscribed in the polygon

  25. Central angle of a circle • An angle whose vertex is at the center of a circle, and whose sides are radii

  26. Central angle of a regular polygon • An angle whose vertex is the center if the regular polygon and whose sides terminate at consecutive vertices of the polygon

  27. Centroid of a triangle • The point at which three medians of the triangle intersect

  28. Chord of a circle • A segment whose end points are on the circle

  29. Circle • The set of all points in a plane at a fixed distance from a given point called the center. The fixed distance is called the radius of the circle. An equation of a circle with center at point (h, k) and radius length r is (x - h²) + (y- k)² = r²

  30. Circumference of a circle • The distance around a circle

  31. Circumscribed circle about a polygon • A circle that passes through each vertex of the polygon

  32. Circumscribed polygon about a circle • A polygon that has all of its sides tangent to the circle

  33. Collinear points • Points that lie on the same line

  34. Common external tangent to two circles • A line that is tangent to both circles, and does not intersect the line segment whose end points are the centers of the two circles

  35. Common internal tangent to two circles • A line that is tangent to both circles, and intersects the line segment whose end points are the centers of the two circles

  36. Complementary angles • Two angles whose measures add up to 90°

  37. Composite transformation • A sequence of two or more transformations in which each transformation after the first is preformed on the image of the transformation that was applied before it

  38. Concentric circles • Circles in the same plane that have the same center but have radii of different lengths

  39. Congruent angles • Angles that have the same measure

  40. Congruent circles • Circles with congruent radii

  41. Congruent line segments • Line segments that have the same length

  42. Congruent polygons • Polygons with the same number of sides that have the same size and same shape. The symbol for congruence is ≅

  43. Congruent triangles • Triangles whose vertices can be paired so that any one on the following conditions is true: (1) the sides of one triangle are congruent to the corresponding sides of the other triangle (SSS ≅ SSS); (2) two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle (SAS ≅ SAS); (3) two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle (ASA ≅ ASA); (4) two angles and the side opposite one of these angles of one triangle are congruent to the corresponding parts of the other triangle ( AAS ≅ AAS). Two right triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts the other triangle (Hy – Leg ≅ Hy – leg)

  44. Converse of a conditional statement • Another conditional statement formed by interchanging the hypothesis (“Given”) with the conclusion (“To Prove”) of the original statement

  45. Convex polygon • A polygon each of whose interior angles measures less than 180°

  46. Coordinate plane • A plane that is divided into four equal regions, called quadrants, by a horizontal number line and a vertical number line, called axes, intersecting at their zero points, called the origin. Each point in a coordinate plane is located by an ordered pair of numbers of the form (x, y). The first member, x, of the ordered pair gives the directed distance of the zero point of the x-axis (horizontal). The second member, y, of the ordered pair gives the directed distance of the point from the zero point of the y-axis

  47. Corollary • A theorem that can easily be proved by means of a closely related theorem

  48. Corresponding angle • Pairs of angles formed when a transversal intersects two lines. The two angles in each pair lie on the same side of the transversal, but one angle is between the two lines, and the other is exterior to the two lines

  49. Cosine of an acute angle of a right triangle • The ratio of the length of the leg that is adjacent to the acute angle to the length of the hypothenuse

  50. Decagon • A polygon with 10 sides

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