Postulates Through any two points there is exactly one line. Through any three noncollinear points there is exactly one plane containing them. If two points lie in a plane, then the line containing those points lies in the plane. If two lines intersect, then they intersect in exactly one point. If two planes intersect, then they intersect in exactly one line. Ruler Post. The points on a line can be put in one-to-one correspondence with the real numbers (we can make any line a number line). Segment Addition Post. We can add segment lengths together when B is between A and C, AB+BC=AC. Protractor Post. We can measure angles in degrees from 0 to 80. Angle Addition Post. When two angles are adjacent, we can add their angle measures together. Corresponding Angles Post. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3 Converse of the Corresponding If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the 3 Angles Post. two lines are parallel. Parallel Post. Through a point not on a line, there is exactly one line parallel to the given line. 3 Side-Side-Side (SSS) Congruence If three sides of one triangle are congruent to three sides of another triangle, then the triangles are 4 congruent. Side-Angle-Side (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of 4 Congruence another triangle, then the triangles are congruent. Angle-Side-Angle (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of 4 Congruence another triangle, then the triangles are congruent. Angle-Angle (AA) Similarity If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. 7 Area Addition Postulate The area of a region is equal to the sum of the areas of its non-overlapping parts. 0 Theorems Pythagorean Thm. In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the, 5 hypotenuse. For legs a and b and hypotenuse c we write: a + b = c. Linear Pair Theorem If two angles form a linear pair, then they are supplementary. Congruent Supplement Thm. If two angles are supplementary to the same angle (or to two congruent angles), then they are congruent. Right Angle Congruence Thm. All right angles are congruent. Congruent Complements Thm. If two angles are complementary to the same angle (or to two congruent angles), then they are congruent. Page
Common Segments Thm. Given collinear points A, B, C, and D arranged as shown: If AB CD, then AC BD Vertical Angles Thm. Vertical angles are congruent. If two congruent angles are supplements, then each angle is a right angle. Alternate Interior Angles Thm. If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 Alternate Exterior Angles Thm. If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 3 Same-side Interior Angles Thm. If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. 3 Converse of the Alternate Interior If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then 3 Angles Thm. the two lines are parallel. Converse of the Alternate If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then 3 Exterior Angles Thm. the two lines are parallel. Converse of the Same-side If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, 3 Interior Angles Thm. then the two lines are parallel. If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular. 3 Perpendicular Transversal Thm. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other 3 line. Equal Measure Linear Pair Thm. If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other. 3 Perpendicular Bisector Thm. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the 3 segment. Converse of the Perpendicular If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the 3 Bisector Thm. segment. Parallel Lines Thm. In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. Any two 3 vertical lines are parallel. Perpendicular Lines Thm. In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is 3. (Their slopes are opposite reciprocals). Vertical and horizontal lines are perpendicular. Triangle Sum Thm. The sum of the angle measures of a triangle is 80 degrees. 4 Exterior Angle Thm. The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior 4 angles. Third Angles Thm. If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles 4 is congruent. The acute angles of a right triangle are complementary 4 The measure of each angle of an equiangular triangle is 60 degrees. 4 Quadrilateral Sum Thm. The sum of the angle measures in a quadrilateral is 360 degrees. 4 Page
Angle-Angle-Side (AAS) If two angles and a non-included side of one triangle are congruent to the corresponding angles and nonincluded 4 Congruence side of another triangle, then the triangles are congruent. Hypotenuse-Leg (HL) If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right 4 Congruence triangle, then the triangles are congruent. Isosceles Triangle Thm. If two sides of a triangle are congruent, then the angles opposite those sides are congruent. 4 Converse of the Isosceles If two angles of a triangle are congruent, then the sides opposite those angles are congruent. 4 Triangle Thm. If a triangle is equilateral, then it is equiangular. 4 If a triangle is equiangular, then it is equilateral. 4 Perpendicular Bisector Thm. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the 5 segment. Converse of the Perpendicular If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector. 5 Bisector Thm. Angle Bisector Thm. If a point is on the angle bisector of a segment, then it is equidistant from the sides of the angle. 5 Converse of the Angle Bisector If a point is in the interior of an angle and equidistant from the sides of an angle, then it lies on the angle 5 Thm. bisector. Circumcenter Thm. The circumcenter of a triangle is equidistant from the vertices of the triangle. 5 Incenter Thm. The incenter of a triangle is equidistant from the sides of the triangle. 5 Centroid Thm. The centroid of a triangle is /3 the distance from each vertex to the midpoint of the opposite side. 5 Triangle Midsegment Thm. A midsegment of a triangle is parallel to a side and half the length of that side. 5 If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. 5 If two angles of a triangle are not congruent, then the longer side is opposite the larger angle. 5 Triangle Inequality Thm. The sum of any two side lengths of a triangle is greater than the third side length. 5 Hinge Theorem (SAS Inequality) If two sides of one triangle are congruent to two sides of another triangle and the included angles are not 5 congruent, then the longer third side is across from the larger included angle. Converse of the Hinge Thm. (SSS If two sides of one triangle are congruent to two sides of another triangle and the included angles are not 5 Inequality) congruent, then the larger included angle is across from the longer third side. Converse of the Pythagorean If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the 5 Thm. third side, then the triangle is a right triangle. Pythagorean Inequalities Thm. In Δ ABC, c is the length of the longest side. If c > a + b, then the triangle is obtuse. If c < a + b, 5 then the triangle is acute. 45-45-90 Triangle Thm. In a 45-45-90 triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg 5 times. 30-60-90 Triangle Thm. In a 30-60-90 triangle, the length of the hypotenuse is times the length of the shorter leg, and the length 5 of the longer leg is the length of the shorter leg times 3. Page 3
Polygon Angle Sum Thm. The sum of the interior angle measures of a convex polygon with n sides is ( n )80. 6 Polygon Exterior Angle Sum The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360, 6 Thm. If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent. 6 If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent. 6 If a quadrilateral is a parallelogram, then the diagonals bisect each other. 6 If a quadrilateral is a parallelogram, then consecutive angles are supplementary. 6 If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a 6 parallelogram. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 6 Trapezoid Midsegment Thm. Angle-Angle (AA~) Similarity If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 6 If an angles of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a 6 parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 6 If a quadrilateral is a rectangle, then it is a parallelogram. 6 If a parallelogram is a rectangle, then its diagonals are congruent. 6 If a quadrilateral is a rhombus, then it is a parallelogram. 6 If a parallelogram is a rhombus, then its diagonals are perpendicular. 6 If a parallelogram is a rhombus, then each diagonal bisects a pair if opposite angles. 6 If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle. 6 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. 6 If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. 6 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus 6 If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. 6 If a quadrilateral is a kite, then its diagonals are perpendicular. 6 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. 6 If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. 6 If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. 6 A trapezoid is isosceles if and only if its diagonals are congruent. 6 The Midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of 6 the bases. If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are 7 similar. Page 4
Side-Side-Side (SSS~) Similarity If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then 7 the triangles are similar. Side-Angle-Side (SAS~) If two sides of one triangle are proportional to two sides of another triangle and their included angles are 7 Similarity congruent, then the triangles are similar. Triangle Proportionality Thm. If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides 7 proportionally. Converse of the Triangle If a line divides two sides of a triangle proportionally, then it is parallel to the third side. 7 Proportionality Thm. Two-Transversal Proportionality If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. 7 Triangle Angle Bisector Thm. An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides. 7 If the similarity ratio of two similar figures is a b, then the ratio of their perimeters is a 7. And the ratio of b a their areas is b. The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to 8 the original triangle. When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric 8 mean between the lengths of the two segments of the hypotenuse. When the altitude is drawn to the hypotenuse of a right triangle, the length of a leg is the geometric mean 8 between the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to the leg. Law of Sines sin sin sin In any triangle Δ ABC, 8 = = a b c Law of Cosines In any triangle Δ ABC, c = a + b abcosc 8 For plane figures, if all dimensions are multiplied by a, then the perimeter (circumference) changes by a 0 factor of a and the area changes by a factor of a. For plane figures, if one dimension is multiplied by a, and another multiplied by b, then the area changes by a factor of ab. 0 Formulas Circumference (of a circle) C = π r or C = π d Area (of a circle) A = π r Page 5
Midpoint Formula For two points on the coordinate plane, (, ) and (, ) Distance Formula For two points on the coordinate plane, ( ) ( ) ( x + x ) ( y + y ) x y x y, the midpoint is M, x, y and x, y, the distance between them is d = ( x x) + ( y y) Slope For two points on the coordinate plane, (, ) and (, ) x y x y, the slope of the line containing them is y y m = x x Equation of a Line Point Slope y y = m( x x) where m is the slope and ( x, y ) is a given point on the line. 3 Form Equation of a Line Slope y = mx + b where m is the slope and b is the y-intercept. 3 Intercept Form Equation of a Line Standard Ax + By = C where A, B, and C are integers and A is positive. 3 Form Area of a Triangle (sine formula) The area of a triangle is absin C 8 3 Area of a Parallelogram The area of a parallelogram with base b and height h is A=bh. 0 Area of a Triangle The area of a triangle with base b and height h is A= bh 0 Area of a trapezoid The area of a trapezoid with bases b and b and height h is ( ) hb+ b 0 Page 6
Area of a Rhombus The area of a rhombus with diagonals d and d is dd 0 Area of a Rhombus The area of a kite with diagonals d and d is dd 0 Area of a Regular Polygon A= ap where a is the apothem and P is the perimeter. 0 Properties Addition Property of Equality If a= b, then a+ c= b+ c Subtraction Property of Equality If a= b, then a c= b c Multiplication Property of Equality If a = b, then ac = bc Division Property of Equality If a b and c 0, then a b = = c c Reflexive Property of Equality a = a Symmetric Property of Equality If a= b, then b= a Transitive Property of Equality If a= b and b= c, then a= c Substitution Property of Equality If a= b, then b can be substituted for a in any expression. Distributive Property ab ( ± c) = ab± ac Reflexive Property of Congruence For figure A, A A Symmetric Property of For figures A and B, if A B, then B A Congruence Transitive Property of For figures A, B, and C, if A B and B C, then A C Congruence Triangle Rigidity If the side lengths of a triangle are given, the triangle can have only one shape. 4 Page 7
Properties Reflexive Property of Similarity ΔABC ΔABC 7 Symmetric Property of Similarity If ΔABC ΔDEF then ΔDEF ΔABC 7 Transitive Property of Similarity If ΔABC ΔDEF and ΔDEF ΔXYZ, then ΔABC ΔXYZ 7 Head-to-Tail method of Vector addition Place the initial point (tail) of the second vector on the terminal point (head) of the first vector. The resultant is the vector that joins the initial point of the first vector to the terminal point of the second vector. 8 Parallelogram method of Vector addition Use the same initial point for both of the given vectors. Create a parallelogram by adding a copy of each vector at the terminal point (head) of the other vector. The resultant vector is a diagonal of the parallelogram formed. 8 Terms Definition Acute angle Measures greater than 0 and less than 90 degrees. Acute triangle A triangle with three acute angles. 4 Adjacent angles Two angles in the same plane with a common vertex and side but no common interior points. Alternate exterior angles Two angles that lie on opposite sides of a transversal and outside the two lines cut by the transversal. 3 Alternate interior angles Two nonadjacent angles that lie on opposite sides of a transversal and in between the two lines cut by the 3 transversal. Altitude (of a triangle) A perpendicular segment from a vertex to the line containing the opposite side of the triangle. 5 Angle A figure formed by two rays with a common endpoint. Angle bisector A ray that divides an angle into two congruent angles. Angle of Depression The angle formed by a horizontal line and a line of sight to a point below the line. 8 Page 8
Terms Definition Angle of Elevation The angle formed by a horizontal line and a line of sight to a point above the line. 8 Apothem The distance from the center of a regular polygon to a side (on the perpendicular) 0 Area The number of non-overlapping square units of a given size that cover a plane figure. Auxiliary Line A line added to a diagram to aid in a proof. 4 Axiom (postulate) A statement that is accepted without proof. Base (of a trapezoid) Each of the parallel sides of a trapezoid. 6 Base (of a triangle) Any side. Base (of an isosceles triangle) The side opposite the vertex angle 4 Base angles (of a trapezoid) Two consecutive angles whose common side is a base. 6 Base angles (of an isosceles The two angles that have the base as a side 4 triangle) Between A point is between two points if it lies on the same line. Biconditional statement The combination of a statement and its converse, written in the form p if and only if q this means if p then q and if q then p. In order for a biconditional statement to be true, both the statement and its converse must be true. Central Angle (of a regular A central angle of a regular polygon has its vertex at the center and its sides pass through consecutive 0 polygon) vertices. Each central angle measure of a regular n-gon is 360 n Centroid (of a triangle) The point of concurrency of the medians of a triangle. It is always in the interior of the triangle and is the 5 point where a triangular region will balance. Circle The locus of points in a plane equidistant from a given point. 0 Circumcenter (of a triangle) The center of the circle circumscribed around a triangle; equidistant from the three vertices of the triangle. 5 The circumcenter is the point of concurrency of the three perpendicular bisectors of the triangle. Circumference (of a circle) The distance around the circle. Circumscribed A circle that contains all the vertices of a polygon is circumscribed around the polygon. 5 Collinear Points that lie on the same line. Complementary Angles Two angles whose measures sum to 90 degrees. Component form (of a vector) The component form ( x, y ) of a vector lists the horizontal and vertical change from the initial point to the 8 terminal point. Composite figure A composite figure is made up of simple shapes such as triangles, rectangles, trapezoids and circles. 0 Concave A polygon such that a diagonal contains points in the exterior of the polygon. 6 Conclusion The part of a conditional statement if p then q that is the logical result; usually the part following then Concurrent When three or more lines intersect at one point, they are concurrent. 5 Conditional (if-then) A statement that can be written in the form if p then q. Page 9
Terms Definition Congruent Having the same shape and size. Congruent polygons Two polygons are congruent iff their corresponding angles and sides are congruent 4 Conjecture A statement believed to be true based on inductive reasoning. Construction A precise method of drawing using only a compass and straightedge. Contrapositive The contrapositive of a conditional statement if p then q is formed by both exchanging and negating the hypothesis and conclusion: if ~q then ~p. Converse The converse of a conditional statement if p then q is formed by interchanging the hypothesis and conclusion: if q then p. Convex A polygon such that no diagonal contains points in the exterior of the polygon. 6 Coordinate The number that corresponds to a point on a number line. Coordinate Plane A plane that is divided into four regions by a horizontal number line (the x-axis) and a vertical number line (the y-axis). Coordinate proof This style of proof uses coordinate geometry and algebra. After positioning the given figure on the 4 coordinate plane, algebra is used to accomplish the steps in the proof. Coplanar Points that lie in the same plane. Corollary A theorem that follow directly from the proof of another theorem. 4 Corresponding angles Two angles that lie on the same side of a transversal and on the same side of the two lines cut by the 3 transversal. Cosine The cosine of an angle is the ratio of the length of the leg adjacent to the angle to the length of the 8 hypotenuse. Counterexample One example of a conjecture that is not true. A counterexample can be a drawing, statement, or number. CPCTC Corresponding Parts of Congruent Triangles are Congruent 4 Decagon A ten-sided polygon. 6 Deductive reasoning A logical argument in which conclusions are drawn from given facts (including theorems and postulates), definitions, and properties. Definition (in geometry) A statement that describes a mathematical object; this can be written as a true biconditional statement. Diagonal (of a polygon) A segment that connects any two nonconsecutive vertices. 6 Diameter (of a circle) A segment that passes through the center of the circle and whose endpoints are on the circle. Dilation A transformation with center O and scale factor k so that when k the resulting image is either an expansion or a contraction of the (original) preimage. 4 Page 0
Terms Definition Direction (of a vector) The direction of a vector is the angle that it makes with a horizontal line, measured counterclockwise from the positive x-axis. The direction of a vector can also be given as a bearing relative to the compass direction north, measured in a clockwise direction (or by using east and west). 8 Distance (between points) The distance between points is the absolute value of the difference of the coordinates. Distance (from a point to a line) The length of the perpendicular (shortest) segment from the point to the line. 3 Dodecagon A twelve-sided polygon. 6 Endpoint A point at one end of a segment or the starting point of a ray. Equal vectors Two vectors are equal if they have the same magnitude and the same direction. 8 Equiangular Triangle A triangle with three congruent angles. 4 Equidistant Equal distance 5 Equilateral Triangle A triangle with three congruent sides. 4 Exterior The set of all points outside the figure. 4 Exterior (of an angle) All points that lie outside the sides of the angle. Exterior Angle The angle formed by one side of a triangle and the extension of an adjacent side. 4 Geometric Mean The geometric mean of two positive numbers is the positive square root of their product. 8 Geometric probability The geometric probability of an event occurring is the length or area of the desired outcome divided by 0 the length or area of the sample space. Height (of a triangle) The segment from a vertex that forms a right angle with a line containing the base of the triangle. Hendecagon An eleven-sided polygon. 6 Heptagon A seven-sided polygon. 6 Hexagon A six-sided polygon. 6 Hypotenuse The side of a right triangle opposite the right angle. Hypothesis The part of a conditional statement if p then q that is the premise; usually the part following if Image The plane figure resulting from a transformation. Incenter (of a triangle) The center of the circle inscribed in a triangle; equidistant from the three sides of the triangle. The 5 incenter is the point of concurrency of the three angle bisectors of the triangle. Included angle An angle formed by two adjacent sides of a polygon. 4 Included side The common side of two consecutive angles in a polygon. 4 Page
Terms Definition Indirect proof A proof written by beginning with the assumption that the conclusion is false. 5 Indirect measurement Any method that uses formulas, similar figures, and/or proportions to measure and object. 7 Inductive reasoning A logical argument that a statement is true because specific, observed cases have been true. Inscribed A circle that is inscribed in a polygon is tangent to the sides of the polygon. (That is, the circle intersects 5 each side in exactly one point.) Interior The set of all points inside the figure. 4 Interior (of an angle) All points between the sides of the angle. Inverse The inverse of a conditional statement if p then q is formed by negating the hypothesis and conclusion: if ~p then ~q. Isometry (rigid motion) A transformation in which distance and angle measure is preserved; a rigid motion. Isosceles Trapezoid A trapezoid with congruent legs. 6 Isosceles Triangle A triangle with at least two congruent sides. 4 Kite A quadrilateral with exactly two pairs of congruent consecutive sides. 6 Law of Detachment When if p then q is a true statement and p is true, then q is true. Law of Syllogism When both if p then q and if q then r are true statements, then if p then r is a true statement. Legs (of a right triangle) The two sides of a right triangle that from the right angle. Legs (of a trapezoid) The nonparallel sides of a trapezoid. 6 Legs (of an isosceles triangle) The two congruent sides are called legs 4 Length The distance between two points is the length of the segment between them. Line Straight path that has no thickness and extends forever. (This is an undefined term, a concept.) Linear Pair Two adjacent angles whose non-common sides are opposite rays. Locus A set of points that satisfies a given condition. 5 Magnitude (of a vector) Measure (of an angle) Page The magnitude of a vector is its length, written AB or u. When a vector is used to represent speed in a 8 given direction, the magnitude of the vector equals the speed. Given in degrees, this is 360 of a circle. Median (of a triangle) A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. 5 Midpoint The midpoint of a segment divides it into two congruent segments. Midsegment (of a trapezoid) The segment whose endpoints are the midpoints of the legs. 6 Midsegment (of a triangle) The segment that joins the midpoints of two sides of the triangle. 5 Negation The negation of a statement p, written ~p, has the opposite truth value as the statement. (The negation of a true statement is false and the negation of a false statement is true). n-gon A polygon with n sides. 6
Terms Definition Nonagon A nine-sided polygon. 6 Noncollinear Points that do not lie on the same line. Noncoplanar Points that do not lie in the same plane. Obtuse angle Measures greater than 90 and less than 80 degrees. Obtuse Triangle A triangle with exactly one obtuse angle. 4 Octagon An eight-sided polygon. 6 Opposite Rays Two rays that have a common endpoint and form a line. Ordered Pair The location or coordinates of a point on the coordinate plane, given by( x, y ). Orthocenter (of a triangle) The point of concurrency of the altitudes of a triangle. 5 Parallel lines Coplanar lines that do not intersect. 3 Parallel planes Planes that do not intersect. 3 Parallel vectors Two vectors are parallel if they have the same direction or if they have opposite directions (they may have 8 different magnitudes). Parallelogram A quadrilateral with both pairs of opposite sides parallel. 6 Pentagon A five-sided polygon. 6 Perimeter The sum of the side lengths of a plane figure. Perpendicular bisector The perpendicular bisector of a segment is a line perpendicular to the segment at the segment s midpoint. 3 Perpendicular Lines Two lines are perpendicular if and only if they form right angles. 3 Perpendicular lines Lines that intersect to form right angles. 3 Plane A flat surface that has no thickness and extends forever. (This is an undefined term, a concept.) Point Names a location and has no size; represented by a dot. (This is an undefined term, a concept.) Point of concurrency The point where three or more lines intersect. 5 Polygon A closed plane figure formed by three or more line segments. Each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear. Postulate (axiom) A statement that is accepted without proof. Preimage The original plane figure. Proof A logical argument that uses definitions, properties, and previously proven statements to show a true conclusion. Proof by contradiction A proof written by beginning with the assumption that the conclusion is false. 5 Pythagorean Triple A set of three nonzero whole numbers a, b, and c such that a + b = c 5 Quadrilateral A four-sided polygon. Radius (of a circle) A segment whose endpoints are the center of the circle and a point on the circle. Ray A part of a line that starts at an endpoint and extends forever in one direction. Page 3
Terms Definition Rectangle A quadrilateral with four right angles. 6 Reflection A transformation (flip) across a line of reflection. Each point and its image are the same distance from the line of reflection. Regular A polygon in which all angles are congruent and all sides are congruent (equiangular and equilateral). 6 Remote Interior Angle An interior angle of a triangle that is not adjacent to the exterior angle. 4 Resultant vector The resultant vector is the vector that represents the sum of two given vectors. To add two vectors 8 geometrically, use the head-to-tail method or the parallelogram method. Rhombus A quadrilateral with four congruent sides. 6 Right angle Measures 90 degrees. Right Triangle A triangle with exactly one right angle. 4 Rigid motion (isometry) A transformation in which distance and angle measure is preserved; an isometry. Rotation A transformation (turn) about a point, or center of rotation. Each point and its image are the same distance from the center of rotation. Same-side interior angles Two angles that lie on the same side of a transversal and in between the two lines cut by the transversal. 3 (consecutive interior angles) Scale The ratio of any length in a drawing to the corresponding actual length. 7 Scale drawing Represents an object as smaller or larger than its actual size. 7 Scale factor Describes how much a figure is enlarged (expanded) or reduced (contracted). Often represented as scale 8 factor k. Scalene Triangle A triangle with no congruent sides. 4 Segment (line segment) Part of a line consisting of points and all the points in between them. Segment bisector A ray, segment, or line that intersects a segment at its midpoint. Side (of a polygon) A segment between consecutive vertices. 6 Similar polygons Two polygons are similar if and only if their corresponding angles are congruent and their corresponding 7 sides lengths are proportional. Similarity ratio The ratio of the lengths of corresponding sides of two similar polygons. 7 Similarity transformation A Transformation that produces similar figures (such as a dilation). 7 Sine The sine of an angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse. 8 Skew lines Noncoplanar lines that do not intersect. 3 Slope The slope of a line is the ratio of rise to run. 3 Solve a triangle Using given measures to find the unknown angle measures and side lengths of a triangle. 8 Straight angle Formed by two opposite rays and measures 80 degrees. Supplementary Angles Two angles whose measures sum to 80 degrees. Page 4
Terms Definition Tangent ratio The tangent of an angle is the ratio of the length of the leg opposite the angle to the lenth of the leg 8 adjacent to the angle. Theorem A statement that can be proven. Once proven, a theorem can be used as a reason in later proofs. Transformation A change in the position, size, or shape of a plane figure that maps a preimage to an image. Translation A transformation (slide) in which all the points of a plane figure move the same distance in the same direction. Transversal A line that intersects two coplanar lines at two different points. 3 Trapezoid X A quadrilateral with exactly one pair of parallel sides. 6 Triangle A three-sided polygon. Truth Value A conditional statement has a truth value of either true (T) or false (F). It is false only when the hypothesis is true and the conclusion is false. Two statements with the same truth value are logically equivalent. Vector A vector is a quantity that has both length and direction. 8 Venn Diagram A drawing with ovals used to represent sets in which the ovals overlap if sets share common elements. Vertex (of a polygon) The common endpoint of two sides of a polygon. 6 Vertex (of an angle) The common endpoint of two rays forming an angle. Vertex angle (of an isosceles The vertex angle is included between the legs 4 triangle) Vertical Angles Two non-adjacent angles formed by two intersecting lines. Page 5