Sasha Vasserman

 Two triangles are similar if two pairs of corresponding angles are congruent

 Two triangles are congruent if two pairs of corresponding angles are congruent and a non-included pair of corresponding sides are congruent

 The x-coordinate of a point in the coordinate plane

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

 An angle whose degree measure is 90

 A triangle with three acute angles

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

 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

 A segment that is perpendicular to the side of the figure to which it is drawn

 The union of two rays that have the same end point

 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

 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

 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

 For a regular polygon, the radius of its inscribed circle

 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

 For a plane geometric figure, the number of square units it contains

 Two triangles are congruent if two pairs of corresponding angles are congruent and the sides included by these angles are congruent

 The congruent angles that lie opposite the congruent sides of an isosceles triangle

 The non-congruent side of the isosceles triangle

 The parallel sides of a trapezoid

 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

 To divide into two equal parts

 The common center of the circles inscribed and circumscribed in the polygon

 An angle whose vertex is at the center of a circle, and whose sides are radii

 An angle whose vertex is the center if the regular polygon and whose sides terminate at consecutive vertices of the polygon

 The point at which three medians of the triangle intersect

 A segment whose end points are on the 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

 The distance around a circle

 A circle that passes through each vertex of the polygon

 A polygon that has all of its sides tangent to the circle

 Points that lie on the same line

 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

 A line that is tangent to both circles, and intersects the line segment whose end points are the centers of the two circles

 Two angles whose measures add up to 90°

 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

 Circles in the same plane that have the same center but have radii of different lengths

 Angles that have the same measure

 Circles with congruent radii

 Line segments that have the same length

 Polygons with the same number of sides that have the same size and same shape. The symbol for congruence is ≅

 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)

 Another conditional statement formed by interchanging the hypothesis (“Given”) with the conclusion (“To Prove”) of the original statement

 A polygon each of whose interior angles measures less than 180°

 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

 A theorem that can easily be proved by means of a closely related theorem

 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

 The ratio of the length of the leg that is adjacent to the acute angle to the length of the hypothenuse

 A polygon with 10 sides

 A step-by-step process by which a set of accepted facts is used to arrive at a conclusion

 A unit of angle measure. One degree is the measure of an angle formed by 1/360 of one complete rotation of a ray about its end point

 A line segment whose end points are nonconsecutive vertices of the polygon

 A chord of the circle that contains the center of the circle

 A size transformation that produces an image similar to the original figure

 An isometry that pressserves orientation

 A formula used to find the length of the segment determined by two points in the coordinate plane. The distance d between two points, A and B, is given by the formula d = the square root of ((X of point B – X of point A)squared + (Y of point B – Y of point A) squared)

 The length of the perpendicular segment from the point to the line

 A polygon with 12 sides

 A polygon in which all the angles have the same measure

 A triangle in which all three angles have the same measure

 Having the same distance

 A polygon in which all the sides have the same length

 A triangle whose three sides have the same length

 An angle formed by a side of the polygon and the extension of an adjacent side of the polygon

 Tangent circles that lie on opposite sides of the common tangent

 The first and fourth terms in a proportion. In the proportion a over b = c over d, a and d are the extremes

 The composition of a reflection in a line and a translation in the direction parallel to the reflecting line

 The set of points in a plane that lie on one side of a line

 A polygon with six sides

 The side of a right triangle that is opposite to the right angle

 The point at which three bisectors of the triangle intersect

 A method of proof in which each possibility except the one that needs to be proved is eliminated by showing that it contradicts some known or given fact

 An angle whose vertex lies on the circle and whose sides are chords of the circle

 A circle that is tangent to each side of the polygon

 A polygon that has all of its vertices on a circle

 Tangent circles that lie on one side of the common tangent

 A transformation that produces an image congruent to the original figure

 A trapezoid whose nonparallel sides called legs, have the same length

 A triangle with two sides, called legs that have the same length

 Either of the two sides of the right triangle that are not opposite the right angle

 A term undefined in geometry; a line can be described as a continuous set of points forming a straight path that extends indefinitely in two opposite directions

 The line segment whose end points are the centers of the circles

 Part of a line that consists of two different points on a line called end points, and the set of all points on the line that ate between them. AB refers to the distance of a line segment with end points A and B, whereas AB with a line of it refers to the segment itself

 When a line can be drawn that divides the figure into two parts that coincide when folded along the line

The set of all points, and only those points, that satisfy a given condition

 An arc of a circle whose degree measure is greater than 180°

 The two middle terms of a proportion. In the proportion a over b = c over d, then either b or c are called the mean proportional between a and d

 A line segment whose end points are the midpoints of the legs of the trapezoid

 A line segment whose end points are a vertex of the triangle and the midpoint of the side opposite that vertex

 A formula used to find the coordinates of the midpoint of a line segment in the coordinate plane. The midpoint of a line segment whose points are A(x, y) and B(X, Y) is ( (x + X over 2) + ( y + Y) over 2))

 The point on a line segment that divides the segment into two segments that have the same length

 An arc of a circle whose degree measure is less than 180°

 An angle whose degree measure is greater than 90° and less than 180°

 A triangle that contains an obtuse angle

 A polygon with eight sides

 An isometry that reverses orientation

 Two rays that have the same end point and form a line

 The y-coordinate of a point in the coordinate plane

 The zero point on a number line

 The point at which the three altitudes of the triangle intersect

 Lines in the same plane that do not intersect

 A quadrilateral that has two pairs of parallel sides

 A polygon with five sides

 The sum of the lengths of the sides of the polygon

 A line, ray, or line segment that is perpendicular to the segment at its midpoint

 Two lines that intersect at 90° angles

 A term undefined in geometry; a plane can be described as a flat surface that extends indefinitely in all directions

 A term undefined in geometry; a point can be described as a dot with no size that indicates location

 A figure with 180° rotational symmetry

 A closed figure in a plane whose sides are line segments that intersect at their end points

 A statement whose truth is accepted without proof

 An equation that states that two ratios are equal. In a proportion, the product of the means equals the product of the extremes

 In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse

 One of the four equal rectangular regions into which the coordinate plane is divided

 A polygon with four sides

 A line segment whose end points are the center of the circle and any point on a circle

 The radius of its circumscribed circle

 A comparison of two numbers by division. The ratio of a to b can be represented by the fraction a over b, provided that b is not equal to zero

 The constant ratio of the lengths of any two corresponding sides

 The part of a line that consists of a fixed point, called an end point, and the set of all points on one side of the end point

 The number that, when multiplied by the original number, gives 1. For example, the reciprocal over 1 over 5 is 5 over 1, AKA, 5. 5 over 1 times 1 over 5 equals 1

 A parallelogram with four right angles

 An isometry that “flips” a figure over a line while reversing orientation

 A parallelogram with four sides that have the same length

 An angle whose degree measure is 90°

 A triangle that contains a right angle

 An isometry that “turns” a figure a specified number of degrees in a given direction (clockwise or counterclockwise) about some fixed point called the center of rotation

 A figure has rotational symmetry if it coincides with its image for some rotation of 180° or less

 Two triangles are congruent if two pairs of corresponding sides are congruent and the angles formed by these sides are congruent

 A triangle in which no two sides have the same length

 A line that intersects the circle in two different points

 An arc whose end points are a diameter of the circle

 Figures that have the same shape but may have different sizes. Two polygons with the same number of sides are similar if corresponding angles are congruent and the lengths of corresponding sides are in proportion

 The ratio of the length of the leg that is opposite the acute angle to the length of the hypotenuse

 A numerical measure of the steepness of a non-vertical line. The slope of a line is the difference of the coordinates of any two different points on the line divided by the difference of the corresponding x-coordinates of the two points. The slope of a horizontal line is 0, and the slope of a vertical line is undefined

 A formula used to calculate the slope of a non-vertical line when the coordinates of two points on the line are given. The slope, m, of a non-vertical line that contains points x and y and X and Y is given by the formula m = Y – y over X - x

 An equation that has the form y = m * x + b, where m is the slope of the line, b is the y-coordinate of the point at which the line crosses the y-axis

 A rectangle all of whose sides have the same length

 Two triangles are congruent if three pairs of corresponding sides are congruent

 Two angles whose measures add up to 180°

 Circles in the same plane that are tangent to the same line at the same point

 The ratio of the length of the leg that is opposite a given acute angle to the length of the leg that is adjacent to the same angle

 A line that intersects the circle in exactly one point, called the point of tangency

 A generalization that can be proved

 A mapping of the elements of two sets where the elements are points such that each point of the object is mapped onto exactly one point called its image and each image point corresponds to exactly one point of the original object called the preimage

 An isometry that “slides” all points of a figure the same distance in the same direction

 A line that intersects two lines at different points

 A quadrilateral with exactly one pair of parallel lines

 A polygon with three sides

 A term that can be described but is so basic that it cannot be defined. The terms point, line, and plane are undefined in geometry

 The point at which two sides of the polygon intersect

 The angle formed by the congruent sides of the isosceles triangle

 Pairs of non-adjacent ( opposite ) angles formed by two intersecting lines

 The capacity of a solid figure as measured by the number of cubic units it contains

 The horizontal number line in the coordinate plane

 The first number in the ordered pair that represents the coordinates of a point in the coordinate plane. The x-coordinate gives the directed horizontal distance of the point from the origin

 The vertical number line in the coordinate plane

 The second number in the ordered pair that represents the coordinates of a point in the coordinate plane. The y-coordinate gives the directed vertical distance of the point from the origin

 The y-coordinate of the point at which a non-vertical line crosses the y-axis