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# Geometry Vocabulary

### Geometry Vocabulary Master Deck

Term | Definition |
---|---|

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. |