Geometry Vocabulary Word Wall Cards

1 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

2 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

3 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.

4 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 .

5 BC segment BC. BC ray BC. BC line BC. BC length of BC. ABC angle ABC. m ABC 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).

6 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.

7 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.

8 It is a dolphin. mammal dolphin mammal True! dolphin 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.

9 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 m 1 = m 2 Definition of congruent angles m 2 = m 1 Symmetric Property of Equality 2 1 Definition of congruent angles Example: (paragraph proof).

10 It is given that 1 2. By the Definition of congruent angles, m 1 = m 2. By the Symmetric Property of Equality, m 2 = m 1. By the Definition of congruent angles, 2 1. Virginia Department of Education 2018 Geometry Mathematics Vocabulary Card 14. Properties of Congruence .. Reflexive Property . If .. , then .. Symmetric Property If , then . If .. and .. , then .. Transitive Property If , then . 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 m A > 90 , then A is an obtuse angle m A = 120 . Therefore, A is an obtuse angle. If p q is a true conditional statement and p is true, then q is true.