Geometry Terms

Biconditional The conjugation of a conditional statement and its converse. p iff q Compound Statement A statement formed by joining two or more statements. p- Raleigh is a city in N.C. q- Raleigh is the capital of N.C. Conclusion In a conditional statement, the statement that immeadiatly follows then. If you buy a car, then you get $1,500 back. Conjecture An educated guess based on known information. 2+x= 5 x=3 Contrapositive The statement formed by negating both the hypothesis and conclusion of the conversion of a conditional statement. Converse The statement formed by exchanging the hypothesis and conclusion of a conditional statement. q to p Counterexample An example used to show that any given statement is not always true. 2+2= 7 because 2+2= 4 Deductive Reasoning A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions. 2(9) using the distributive property, you can logically conclude it's 18. Hypothesis In a conditional statement, the statement that immeadiatly follows the word if. If lines m and n never intersect, then they are parallel. Inverse The statment formed by negating both the hypothesis and the conclusion of a conditional statement Negation If a statement is represented by P, then not P is the negation of the statment Properties Can be used to justify each step when solving equations Theorem A statment or conjecture that can be proven true by undefined terms, definitions, and postualtes Alternate Exterior Angles In the figure,<1 and <7 and <2 and <8. Alternate Interior Angles In the figure, <3 and <4 and <6 and <5. Consecutive Interior Angles In the figure,< 1 and < 4 and <5 and <8. Corrosponding Angles In the figure,< A and Parallel Lines Coplanar lines that do not inter sect Lines a and b are parallel Parallel Planes Planes that do not intersect Skew Lines Lines that do nto intersect and are not coplanar Lines RY and SZ. Transversal A line that intersects 2 or more lines in a plane at different points Line t is the transversal. Acute Triangles a triangle in which all of the angles are acute angles Altitude of a traingle a segment from a vertex of the triangle to the line cointaining oppisite sides and perpendicular to that side Red line is altitude. Base Angles 2 angles formed by the base and 1 congruent side < A and < C are base angles. Centroid the point of concurrency of the medians of a triangle G is the centroid. Circumcenter The point of concurrency of the perpendicular bisectors of a triangle Congruence Slide, turn, or flip a triangle to prove this Congruent Triangles Triangles that have their corrosponding parts congruent Coordinate Proof A proof that uses figures in the coordinate plane and algebra to prove geometric concepts Corollary A statment that can be easily proven by using a theorem This is an equilateral triangle because it has all sides and angles equal. Equiangular triangle triangle with all angles congruent All angles are 60 degrees. Equilateral Triangle triangle with all sides congruent All sides are congruent. Exterior angle An angle formed by 1 side of the triangle and the extension of the other side All of the larger 120 degree angles. Hypotenuse the side opposite of the right angle The longest part of the triangle. Incenter The poitn on coincurrency of the angle bisectors of a triangle Point in the middle of a circle. Isosceles At least 2 sides of the triangle are congruent The two sides are congruent. Legs of a right triangle The lines that are part of the right angle Parts that aren't the hypotenuse. median of a triangle a line segment with endpoints that are a vertex of a triangle and tje midpoint of the side opposite of the vertex. AD is a median of the triangle. obtuse triangle one angle is obtuse This triangle is obtuse because it has one 115 degree angle in it. perpendicular bisector a line, segment, or ray that passes through the midpoint of a side and it perpendicular to that side .Red line is perpendicular bisector. point of concurrency the point of intersection of concurrent lines remote interrior angle interior angles of the triangle not adjacent to a given exterior angle.A and C are remote interrior angles. right triangle triangle with a right angle scalene no two sides are congruent vertex angles the angles formed by the congruent sides included angle in a triangle, the angle formed by two sides is the included angle for those two sides included side the side of a triangle that is a side of each of the two angles indirect reasoning reasoning that assumes that the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis. ex: -2 +1= 1 because -2 +1= -1 indirect proof an indirect proof, one assumes that the statement to be proved is false. True or False: False That isn't an acute angle. concave a polygon for which there is a line containing a side of the polygon that also contains a point in the interior of a polygon. convex a polygon for which there is no line that contains both a side of the polygon and the point in the interior of a polygon. mid-segment of a triangle a segment with endpoints that are midpoints of two sides of a triangle. polygon a closed figure formed by a finite number of coplanar segments. proportion an equation of the form a/b = c/d that states two ratios are equal ex: 5/10 = 1/2 regular a convex polygon in which all of the sides are congruent and all of the angles are congruent scale factor the ratio of two lengths of two corresponding sides of two similar polygons or two similar solids similar polygons two polygons are similar iff their corresponding angles are congruent and the measure of their corresponding sides are proportional angle of depression the angle between the line of sight and the horizontal when an observer looks downwards angle of elevation the angle between the line of sight and horizontal when an observer looks upwards altitude of a right triangle a segment from a vertex of the triangle to the line containing the opposite side and perpendicular of that side BD is the altitiude of the right triangle. cosine for an acute angle if a right triangle the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse geometric mean for any positive numbers, a + b, the positive number such that a/x = x/b ex. a / x = x / b Pythagorean triple a group of whole 3 numbers that satisfies the equation a squared + b squared = c squared ex: 3 squared + 6 squared = 9 squared sine for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle over the hypotenuse solving a triangle finding the measures of all the angles and sides of a triangle tangent ratio of the legs of a triangle trigonometry the study of the properties of triangles and trigonometric functions and their applications arc a part of a circle that is defined by two endpoints center a given point in the middle of a circle central angle an angle that intersects a circle in two points and its vertex is at the center of a circle chord a segment with endpoints that are on the circle circle the locus of all points in a plane equidistant from a given point called the center of a circle circumference distance around a circle ex: pi r squared circumscribed a circle is circumscribed about a polygon if the circle contains all of the verticies of the polygon diameter a chord that pssses through the center of a circle inscribed if each of the vertices lie on a circle intercepted iff the endpoints of the arc lie on the angle major arc an arc with a measure greater than 180 The blue line is the major arc. minor arc an arc with a measure less than 180 Red arc is a minor arc because its less than 90 degrees. pi an irrational number represented by the ratio of the circumference of a circle to the diameter of a circle point of tangency for a line that intersects a circle in only one point, the point at which they intersect radius any segment with endpoints that are in the center of the circle secant any line that intersects a circle at exactly two points semicircle an arc that measures 180 degrees tangent a line in the plane of a circle that intersects the circle in exactly one point apothem a segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon geometric probability using the principles of length and area to find the probability of an event irregular figure a figure that can't be classified as a regular polygon irregular polygon a polygon thats not regular sector of a circle a region of a circle bounded by a central angle and its intercepted arc segment of a circle the region of a chord bounded by an arc and a chord consecutive angles of a quadrilateral any two angles whose vertices are the endpoints of the same side A and C are consecutive angles. decagon 10 sided figure diagonal a segment that connects any two nonconsecutive vertices dodecagon 12 sided figure exterior angles of a polygon add up to 360 degrees hexagon 6 sided figure heptagon 7 sided figure interior angles of a polygon add up to 360 degrees on the outside isoceles trapezoid if the legs are congruent kite quadrilateral with two disjointed pairs of congruent adjacent sides median of a trapezoid the segment that joins midpoints of the legs of a trapezoid n-gon polygon with n- sides nonagon 9 sided figure octagon 8 sided figure opposite angles of a quadrilateral any two angles that are not consecutive opposite sides of a quadrilateral any two sides that intersect parallelogram a quadrilateral with parallel opposite sides pentagon 5 sided figure perimeter length of a boundary: ex: a rectangle 2 by 2 , the perimeter is 8 quadrilateral having 4 sides rectangle a quadrilateral with 4 right angles rhombus a quadrilateral with all 4 sides are congruent square if a quadrilateral is both a rhombus and a rectangle trapezoid a quadrilateral with exactly one pair of parallel sides bases of a trapezoid the parallel sides AB and DC are bases of the trapezoid. height of a trapezoid sides that aren't parallel altitude of a 3D figure a segment perpendicular to the bases with endpoints in each plane bases bottom of a figure This figure has a square base. congruent solids 2 solids are congruent if all of the following conditions are met, plane as the base, and a lateral surface area composed of all points in the segments connecting the vertex to the edge of the base cylinder a figure with bases that are formed by congruent circles in parallel planes edges a line or border at which a surface terminates face a face of the polygon that make up its boundaries great circle the intersection of the sphere and a plane that contains the center of the sphere height the distance between the highest and lowest point of a figure acute angle an angle with a measure less than 90 degrees obtuse angle an angle with a measure greater than 90 degrees hemisphere one of the two congruent parts into which a great circle seperates a sphere lateral area the area of the figure not including the bases lateral faces faces that aren't bases nets a 2-dimensional figure that when folded forms the surface of a 3-dimensional object oblique cone a cone that isn't a right cone oblique cylinder a cylinder that is not right platonic solids 5 regular polyhedra dodecahedron a solid figure having 12 faces hexahedron a solid having 6 faces icosahedron a solid having 20 faces octahedron a solid having 8 faces tetrahedron a solid having 4 sides polyhedron closed 8 dimensional figures made up of flat polygonal regions prism a solid with 2 bases, 2 lateral faces, and lateral edges pyramid a solid with all faces intersecting at a vertex, a base, and lateral face regular cone right cone with bases that are regular polygons regular prism right prism with bases that are regular polygons regular cylinder a cylinder with an altitude thats also an axis right cone a cone with an axis thats also an altitude right cylinder a cylinder with an altitude thats also an axis right prism a prism with lateral edges that are also altitudes similar solids solids that have the exactly the same shape, but not necessarily the same size slant height the altitude of the side of a regular pyramid sphere the set of all points that are given distance from a given point surface area the sum of the areas of all faces and side surfaces of a 3-dimensional figure volume a measure of the amount of space enclosed by a 3- dimensional figure vertices of a 3D object the points on a graph center of dilation the fixed point in the plane about whuch all points are expanded or contracted center of rotation a point or line around which all other points in a body move column matrix In linear algebra, a column vector or column matrix is an m × 1 matrix, i.e. a matrix consisting of a single column of elements. columns of a matrix line up to form points on an object composition the act of combining parts and elements to form a whole dilation the act or process of expanding identity matrix image to resemble isometry a function from one metric space onto a second metric space having the property that the distance between two points in the first space is equal to the distance between the image points in the second space mapping function pre-image the point or set of points in the range corresponding to a designated point in the domain of a given function reflection the replacement of each point on one side of a line by the point place symmetrically on the other line reflection matrix rotation an operation that rotates an object around a fixed point rotation matrix row matrix a matrix with only one row scalar a number , numerical quantity , or elment in a field standard matrix translation moving every point a constant distance in a specified direction translation matrix a matrix represnting a translated figure vertex matrix If a graph has vertices, we may associate an matrix distance the greatest lower bound of differences from one point to another perpindicular lines forms four 90 degree angles acute triangle acute triangle a triangle that has all angles less than 90 degrees exterior exterior outer ;external plane a flat surface extending indefinately in all directions interior on the inside point a geometric element that has position but no extension angle the figure formed by two rays sharing a common endpoint line a series of points postulate a declaration of something self-evident angle bisector angle bisector divides the angle into two equal or congruent parts line segment a line that is bounded by 2 endpoints ray a line that extends indefinately in one direction colr collinear lying on the same line linear pair add up to 180 degrees linear pair add up to 180 degrees right angle adds up to 90 degrees complementary angles are angles next to each other that form 90 degrees midpoint a point equidistant from the ends of a line segment bisector any line, segment, or ray that intersects a segment at its midpoint congruent same shape and same size space the set of all points coplanar lying in the same plane Q and B are coplanar . opposite rays form a line supplementary angles add up to 180 degrees degree used to measure angles perpendicular bisector makes 4 right angles undefined terms points, lines, and planes vertex the point of intersection of lines or points opposite the base of the figure vertical angles the pair of angles that are directly across from each other when two straight lines intersect flow proof putting the statements in boxes then putting arrows showing the most logical way to prove the proof if-then statement the words that follow the if are the if statement and the words that follow the then statement are the then statement ex: If all squares are rectangles then all rectangles aren't squares. inductive reasoning reasoning from detailed facts to general principles paragraph proof explaning the proof using sentences and paragraphs proof any factual evidence to establish the truth of something properties something a shape or any figure can have statement a message that is stated or declared two-column proof two columns explaining why you did what you did to solve the proof equidistant the same amount of space apart included angle angle made by two sides with a common vertex included side the common leg of two angles hypotenuse leg theorem proving right triangles similar or congruent CPCTC theorem proving that congruent parts of congruent triangles are congruent SAS theorem proving triangles congruent by side angles side SSS theorem proving triangles congruent by side side side ASA postulate proving triangles congruent by angle side angle AAS postulate proving triangles congruent by angle angle side indirect proof a proof in which one false assumption is made indirect reasoning reasoning using the law of Contrapositive, and negating overlapping triangles triangles that are on top of each other extremes the greatest degree of intensity or extent means the averages ratio the relative magnitude of 2 quantities Law of Sines used to find angles of a general triangle Law of Cosines used to find one side of a triangle when an angle and the other side is known Unit Circle a circle with a radius of one undecagon an eleven sided polygon common external tangent a common tangent that is common in two circles and doesn't intersect the center of the two circles common internal tangent a line that is common in two circles and intersects the center of the two circles concentric circles two or more circles that have the same center and different radii externally tangent circles two circles that aren't inside of each other inscribed angles angles whose vertex is on the circle and whose sides are chords of the circle inscribed figure an inscribed shape inside of the circle internally tangent circles two circles, one of which is inside the other The end :)