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Geometry Vocabulary Word Wall Cards Geometry Vocabulary Word Wall Cards Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development. The cards should be used as an instructional tool for teachers and then as a reference for all students. Table of Contents Reasoning, Lines, and Slope of Lines in Coordinate Plane Distance Formula Transformations Line Symmetry (Examples) Basics of Geometry 1 Point Symmetry (Examples) Basics of Geometry 2 Rotation (Origin) Geometry Notation Reflection Logic Notation Translation Set Notation Dilation Conditional Statement Perpendicular Bisector Converse Constructions: Inverse o A line segment congruent to a given line Contrapositive segment Symbolic Representations in Logical Arguments o Perpendicular bisector of a line segment Conditional Statements and Venn Diagrams o A perpendicular to a given line from a point Deductive Reasoning not on the line Inductive Reasoning o A perpendicular to a given line at a point on Direct Proofs the line Properties of Congruence o A bisector of an angle Law of Detachment o An angle congruent to a given angle Law of Syllogism o A line parallel to a given line through a Counterexample point not on the given line Perpendicular Lines o An equilateral triangle inscribed in a circle Parallel Lines o A square inscribed in a circle Skew Lines o A regular hexagon inscribed in a circle Transversal Corresponding Angles Triangles Alternate Interior Angles Classifying Triangles by Sides Alternate Exterior Angles Classifying Triangles by Angles Consecutive Interior Angles Triangle Sum Theorem Parallel Lines Exterior Angle Theorem Midpoint (definition) Pythagorean Theorem Midpoint Formula Angle and Sides Relationships Find a Missing Endpoint Triangle Inequality Theorem Slope Formula Virginia Department of Education 2018 Geometry Mathematics Vocabulary Congruent Triangles Isosceles Trapezoid SSS Triangle Congruence Postulate Circle SAS Triangle Congruence Postulate Circles – Inscribed HL Right Triangle Congruence Circle Equation ASA Triangle Congruence Postulate Lines and Circles AAS Triangle Congruence Theorem Secant Similar Polygons Tangent Similar Polygons and Proportions Central Angle AA Triangle Similarity Postulate Measuring Arcs SAS Triangle Similarity Theorem Arc Length SSS Triangle Similarity Theorem Secants and Tangents Altitude of a Triangle Inscribed Angle Median of a Triangle Area of a Sector Concurrency of Medians of a Triangle Inscribed Angle Theorem 1 30°-60°-90° Triangle Theorem Inscribed Angle Theorem 2 45°-45°-90° Triangle Theorem Inscribed Angle Theorem 3 Trigonometric Ratios Segments in a Circle Inverse Trigonometric Ratios Segments of Secants Theorem Area of a Triangle Segment of Secants and Tangents Theorem Polygons and Circles Three-Dimensional Figures Polygon Exterior Angle Sum Theorem Cone Polygon Interior Angle Sum Theorem Cylinder Regular Polygon Polyhedron Properties of Parallelograms Similar Solids Theorem Rectangle Sphere Rhombus Hemisphere Square Pyramid Trapezoid Virginia Department of Education 2018 Geometry Mathematics Vocabulary Basics of Geometry 1 Point – A point has no dimension. P It is a location on a plane. It is represented by a dot. point P Line – A line has one dimension. It is an infinite set of points represented by a line with two arrowheads that extend without end. m A B AB or BA or line m Plane – A plane has two dimensions extending without end. It is often represented by a parallelogram. N A plane ABC or plane N C B Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 1 Basics of Geometry 2 Line segment – A line segment consists of two endpoints and all the points between them. A B AB or BA Ray – A ray has one endpoint and extends without end in one direction. C BC B Note: Name the endpoint first. BC and CB are different rays. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 2 Geometry Notation Symbols used to represent statements or operations in geometry. BC segment BC BC ray BC BC line BC BC length of BC ABC angle ABC m measure of angle ABC ABC triangle ABC || is parallel to is perpendicular to is congruent to is similar to Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 3 Logic Notation ⋁ or ⋀ and → read “implies”, if… then… ↔ read “if and only if” iff read “if and only if” ~ not ∴ therefore Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 4 Set Notation { } empty set, null set ∅ empty set, null set x| read “x such that” x: read “x such that” ⋃ union, disjunction, or ⋂ intersection, conjunction, and Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 5 Conditional Statement a logical argument consisting of a set of premises, hypothesis (p), and conclusion (q) hypothesis If an angle is a right angle, then its measure is 90. conclusion Symbolically: if p, then q p→q Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 6 Converse formed by interchanging the hypothesis and conclusion of a conditional statement Conditional: If an angle is a right angle, then its measure is 90. Converse: If an angle measures 90, then the angle is a right angle. Symbolically: if q, then p q→p Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 7 Inverse formed by negating the hypothesis and conclusion of a conditional statement Conditional: If an angle is a right angle, then its measure is 90. Inverse: If an angle is not a right angle, then its measure is not 90. Symbolically: if ~p, then ~q ~p→~q Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 8 Contrapositive formed by interchanging and negating the hypothesis and conclusion of a conditional statement Conditional: If an angle is a right angle, then its measure is 90. Contrapositive: If an angle does not measure 90, then the angle is not a right angle. Symbolically: if ~q, then ~p ~q→~p Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 9 Symbolic Representations in Logical Arguments Conditional if p, then q p→q Converse if q, then p q→p if not p, Inverse ~p→~q then not q if not q, Contrapositive ~q→~p then not p Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 10 Conditional Statements and Venn Diagrams Original Conditional Statement Converse - Reversing the Clauses If an animal is a dolphin, If an animal is a mammal, then then it is a mammal. it is a dolphin. mammal dolphin dolphin mammal True! False! (Counterexample: An elephant is a mammal but is not a dolphin) Inverse - Negating the Clauses Contrapositive - Reversing and Negating the Clauses If an animal is not a dolphin, If an animal is not a mammal, then it is not a mammal. then it is not a dolphin. not mammal not dolphin not False! dolphin True! not (Counterexample: A mammal whale is not a dolphin but is still a mammal) Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 11 Deductive Reasoning method using logic to draw conclusions based upon definitions, postulates, and theorems Example of Deductive Reasoning: Statement A: If a quadrilateral contains only right angles, then it is a rectangle. Statement B: Quadrilateral P contains only right angles. Conclusion: Quadrilateral P is a rectangle. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 12 Inductive Reasoning method of drawing conclusions from a limited set of observations Example: Given a pattern, determine the next figure (set of dots) using inductive reasoning. Figure 1 Figure 2 Figure 3 The next figure should look like this: Figure 4 Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 13 Direct Proofs a justification logically valid and based on initial assumptions, definitions, postulates, and theorems Example: (two-column proof) Given: 1 2 Prove: 2 1 Statements Reasons 1 2 Given m1 = m2 Definition of congruent angles m2 = m1 Symmetric Property of Equality 2 1 Definition of congruent angles Example: (paragraph proof) It is given that 1≅2. By the Definition of congruent angles, m 1 = m2. By the Symmetric Property of Equality, m2 = m1. By the Definition of congruent angles, 2≅1. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 14 Properties of Congruence 퐴퐵̅̅̅̅ 퐴퐵̅̅̅̅ Reflexive Property ∠퐴 ≅ ∠퐴 If 퐴퐵̅̅̅̅ ≅ ̅퐶퐷̅̅̅ , then ̅퐶퐷̅̅̅ ≅ 퐴퐵̅̅̅̅. Symmetric Property If ∠퐴 ≅ ∠퐵, then ∠퐵 ≅ ∠퐴 If 퐴퐵̅̅̅̅ ≅ ̅퐶퐷̅̅̅ and ̅퐶퐷̅̅̅ ≅ 퐸퐹̅̅̅̅, then 퐴퐵̅̅̅̅ ≅ 퐸퐹̅̅̅̅. Transitive Property If ∠퐴 ≅ ∠퐵 푎푛푑 ∠퐵 ≅ ∠퐶, then ∠퐴 ≅ ∠퐶. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 15 Law of Detachment deductive reasoning stating that if the hypothesis of a true conditional statement is true then the conclusion is also true 120 A Example: If mA > 90°, then A is an obtuse angle mA = 120 Therefore, A is an obtuse angle. If pq is a true conditional statement and p is true, then q is true. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 16 Law of Syllogism deductive reasoning that draws a new conclusion from two conditional statements when the conclusion of one is the hypothesis of the other Example: 1. If a rectangle has four congruent sides, then it is a square. 2. If a polygon is a square, then it is a regular polygon. 3. If a rectangle has four congruent sides, then it is a regular polygon. If pq and qr are true conditional statements, then pr is true. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 17 Counterexample specific case for which a conjecture is false Example: Conjecture: “The product of any two numbers is odd.” Counterexample: 2 ∙ 3 = 6 One counterexample proves a conjecture false. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 18 Perpendicular Lines two lines that intersect to form a right angle m n Line m is perpendicular to line n. m n Perpendicular lines have slopes that are negative reciprocals. Virginia Department of Education 2018 Geometry Mathematics Vocabulary – Card 19 Parallel Lines coplanar lines that do not intersect m n m||n Line m is parallel to line n.
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