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# Geometry Vocabulary

### Geometry Vocabulary Master Deck

TermDefinition
Point The most basic of all geometric figures. It has no size or shape. It is represented by a dot and is denoted using a capital letter. It is infinitely small. It does not exist in real life, but is merely used to define other terms.
Line A geometric figure which extends in 2 directions without ending. Referred to by using 2 points on the line and a line symbol above. Is infinitely long and has infinite # of points. It does not exist in real life, but is merely used to define other terms.
Line Segment (Has measurable length). A portion of a line which contains endpoints and all points between them. Referred to using the 2 endpoints and segment symbol above letters. Has infinite # of points, lower level of infinity than line. X exist in real life, is used to define other terms.
Plane A set of points that suggests a surface. The surface is flat, extends without ending, and has no thickness. It is labeled with a capital letter. It extends in infinitely many directions.
Circle A circle with radius r and center o is the set of all points that are a distance r units from o. Encompasses all the points a set distance from a point. That distance is the radius and that point is the center. Has infinite # of points, no edges or sides.
Parallel Lines Lines in the same plane that do not intersect. The notation for parallel is II. Parallel lines have the same slope.
Skew Lines Lines not in the same plane that do not intersect.
Segment Bisector A line, segment, ray, or plane that intersects the midpoint of a segment. Midpoint does splitting, not bisector.
Perpendicular (The slopes of perpendicular lines are opposite reciprocals). 2 lines, rays, or segments that intersect to form a 90° angle. Notation for perpendicular is an upside-down T. Definition is biconditional: 2 lines are perpendicular if and only if they form a right angle. In an angle, a box means perpendicular, not 90°.
Perpendicular Bisector A line through the midpoint of a segment that is perpendicular to that segment.
Orthogonal Derived from Latin: ortho - to be measured at 90 degrees/to be straight, gon - angles. Multiple perpendicular lines (I think so)
Inscribe (any shape with congruent diagonals can be inscribed in a circle. Some kites can be inscribed because they have symmetry even if their diagonals are not equal) Derived from Latin: in - within, scribed - to be written/drawn. When a shape fits inside a circle and EVERY VERTICE TOUCHES THE CIRCLE, is considered inscribed. You can inscribe any regular polygon into circle. Rhombi can only be inscribed when a square.
Kite A shape with 2 distinct pairs of congruent sides.
Angle Bisector A line or ray that goes through the vertex of an angle that divides the angle into 2 equal angles. If D is the bisector of angle ABC, angle ABD and angle DBC are equal.
Rigid Transformation (the image of a figure will be the same if the figure was translated parallel to a reflection line then reflected over the line compared to reflecting over the line then applying the same parallel translation) A translation, reflection, or rotation. A movement that maps a shape to an equal sized shape. Just like there is an order of operations, there is an order of transformations.
Assertion (the image of a figure will NOT be the same if the figure was translated NOT parallel to a reflection line then reflected over the line compared to reflecting over the line then applying the same NON parallel translation) A statement that you think is true but have not yet proven.
Congruent 2 object that have same size+same shape.Symbol is combination of = for same size and ~ for similar shape Times to and to not use ≅ symbol NO use when comparing measurement because do not include shape Whenever 2 figures (segments,∠) have same size+shape,≅
Pre-Image A geometric object before a transformation has been applied.
Image A geometric object after a transformation has been applied. Pre-image points and image points are not the same points. The same letter is usually only used to demonstrate the corresponding points.
Postulate A statement that is accepted without proof (common sense).
Theorem A statement that has to be proven before it is accepted as true.
Isometry Derived from Latin: iso - equal or the same, metry - measure. A transformation that preserves congruence. All rigid transformations are isometric.
Translation (<x±h, y±k>) (<change along x-axis, change along y-axis>) (T: A(x, y) ---> A'(x±a, y±b) A rigid transformation in which all points of pre-image slide same distance in same direction at same time. Translations are made by sliding geometric figure along a vector, a directed line segment with a horizontal and a vertical component of movement.
Reflection (when an image is the same point as its pre-image, still label the point as also its image label.) (Ry=mx+b: A(x, y) ---> A'(x±a, y±b) (Reflection y=mx+b: A ---> A') A reflection is a transformation in which a line of reflection acts like a mirror, reflecting points to their images. The line of reflection is the perpendicular bisector of the segment connecting a pre-image point to its corresponding image.
Rotation R(x, y), z: A(x, y) ---> A' (x±a, y±b) (does not matter + or - when 180) (rotations x reflections) (in 90, slopes of lines from (pre)image points to point of rotation are opposite reciprocals/perpendicular) (in 180, lines are same) A transformation such that all points of a pre-image move through x degrees about a point. Rotation (0, 0), 90 is a rotation 90° counterclockwise around the origin. Rotation (0, 0), -90 is a rotation 90° clockwise around the origin.
Symmetry A figure has symmetry if there is a rigid transformation that maps a pre-image to itself. Excluding the transformations that leave every point where it is.
Reflection Symmetry A figure has reflection symmetry if there is a reflection that maps a figure to itself. The reflection occurs over a line of symmetry.
Rotation Symmetry A figure has rotation symmetry if there is a rotation that maps a pre-image onto itself. Excluding rotations of 0° and 360° because there is no rotation.
If-Then Statement (conditional statement or conditionals) Statements that form a hypothesis and make a conclusion. The conclusion may or may not be correct. The statement is in the form "If hypothesis, then conclusion".
Converse Formed by interchanging hypothesis and conclusion. Ex. Conditional: "If it is raining outside, then it is cloudy." Converse: "If it is cloudy, then it is raining outside." Statement and its converse say different things. Some true statements have false c.
Counterexample An example that is used to disprove an if-then statement (the hypothesis is true but the conclusion is false). Ex. It might not be raining, just cloudy.
Biconditional Ex: Statement: "If segments are congruent, then they have equal lengths." Converse: "If segments have equal lengths, then they are congruent." Biconditional: "Segments are congruent if and only if they have equal lengths." A single statement where the conditional and its converse are both true. The new single statement can be made using the words "if and only if".
5 Essential Elements to a Proof 1. Hypothesis (Given) 2. Conclusion 3. List of sequential reasons 4. List of sequential statements 5. Diagram
Adjacent Angles 2 angles in a plane that share a common vertex and a common side but no common interior points.
Complementary Angles 2 angles whose measures have the sum of 90°. Only refers to a pair, or 2 angles. Angles do not have to be adjacent. 90-x=angle's complement.
Supplementary Angles 2 angles whose measures have the sum of 180°. Only refers to a pair, or 2 angles. Angles do not have to be adjacent. 180-x=angle's supplement.
Vertical Angles 2 angles such that the sides of one angle are opposite rays to the sides of the other angle. When 2 lines intersect they form vertical angles.
Intersection The points that figures have in common.
Transversal A line that intersects 2 or more coplanar lines in different points.
Alternate Interior/Exterior Angles 2 Non-Adjacent Interior/Exterior Angles on opposite sides of the transversal. This definition still applies whether or not the 2 lines are parallel.
Same-Side Interior/Exterior Angles 2 Interior/Exterior Angles on the same side of the transversal. This definition still applies whether or not the 2 lines are parallel.
Corresponding Angles 2 angles in corresponding positions relative to the 2 lines. This definition still applies whether or not the 2 lines are parallel.
Triangle Formed by 3 segments joining 3 non-colinear points. Each of 3 points=vertex, segments=sides. Denoted with △. Scalene=NO≅sidesIsosceles=AT LEAST 2≅sidesEquilateral=3≅sidesalso isos.Acute=3acuteanglesObtuse=1obtuseangleRight=1right angleEquiangular=3≅angles
Corollary Extensions of theorems that include very specific cases.
Congruent Triangles 2 △ are ≅ if and only if their ver. can be matched up socorr. parts (angles, sides) of △ are ≅.In△ABCand △DEF, if ∠ABC corr. and is ≅ to ∠DEF, ∠ABC NO corr. ∠FED cause A + F, C + D no corr.Inotherwords,when△are≅,thever.match up,creatingcorr.∠andcorr.sides
Congruent Polygons 2 polygons are congruent if and only if their vertices can be matched up so that the corresponding parts (angles and sides) are congruent.
Median (of a triangle) A segment from a vertex of the triangle to the midpoint of the opposite side. Note: Every triangle has 3 medians.
Centroid (of a triangle) The intersection of all 3 medians of a triangle. Note: This is the center of gravity of the triangle.
Altitude (of a triangle) A perpendicular segment from a vertex of △ to line that contains opposite side. Every triangle 3 altitudes. Use of phrase "...line that contains opposite side..." implies perpendicular segment does not need to intersect actual opposite side/segment.
Orthocenter (of a triangle) The intersection of all 3 altitudes of a triangle. Note: The orthocenter of a right triangle is the vertex of the right angle of the triangle.
Circumcenter (of a triangle) The intersection of all 3 perpendicular bisectors of the sides of the triangle. Note: The circumcenter of a triangle is equidistant to all 3 vertices of the triangle.
Incenter (of a triangle) The intersection of all 3 angle bisectors of the angles of the triangle. Note: The incenter of a triangle is the center of a circle inside the triangle.
Created by: tianm27
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