Vocabulary Word Lists

Vocabulary Word Lists – Mr. Hanson

You should know the meaning of each of these words, as they apply to your class. Return to main page

Terms printed in blue are important; you are expected to know these!!

Be careful!! Some words may have a different meaning in normal conversation than they do in math!!

Chapter 1 Chapter 2 Chapter 3 Chapter 4

Hierarchy	An ordered arrangement of things or ideas, with some being more basic and others more significant
Abstraction	Existing primarily in the mind rather than in the ‘real’ or natural world. See the Wikipedia article on Abstract Geometric Art.
Angle; straight angle	A geometric figure on a plane made by the intersection of two rays. The intersection point is the vertex; the two rays are the sides of the angle. A straight angle has sides that correspond to a straight line; it has a measure of 180º.
Aristotle	Greek philosopher (384BC-322BC) who, among other achievements, first stated the rules of logic.
Bisector	A line, ray, or segment that divides another object into two congruent pieces.
Collinear	Lying on a single line; any two points are always collinear. Usually we say three or more points are collinear if there is one straight line through all the points.
Congruence	Geometric objects are congruent if they have the same size and shape; distinct from numbers, quantities, or measures which are equal if they have the same size or magnitude.
Coplanar	Lying on a single plane
Equidistant	Being an equal distance from two or more different points or objects.
Euclid	Greek mathematician (325BC-265BC) who first used logic and geometric concepts to create a coherent system of mathematical thought in his book Elements.
Line (Straight)	The shortest path between any two points, and all other points that are collinear. A line in Euclid is considered infinitely long, and having only one dimension, length.
Line Segment	A portion of a line lying between two endpoints.
Logic	The use of reason and careful assumptions to make conclusions about the world or ideas. The process of using our power of reason to make and evaluate statements and arguments.
Midpoint	The unique point on a line segment which is equidistant from the two endpoints of the segment.
Plane	The collection of all lines which connect a given line and any point not on the line. Planes are flat surfaces having two dimension, length and breadth.
Point	An abstract geometric concept of something with no dimension, only location.
Postulate	An assumption, stated and believed to be true, but which cannot be (or is not) proven. (Also called an axiom).
Ray	A portion of a line which begins at a point and extends indefinitely in a given direction.
Space	The collection of all possible lines which connect a plane and a point not on the plane. Space has 3 dimensions: length, breadth, and depth (or height, width and depth).
Theorem	A fact which has been proven true using logic, postulates, and/or other theorems.
Vertex	The point of intersection of the sides of an angle.

Chapter 2: Deduction & Logic:

Angle Bisector	A line, segment, or ray which divides an angle into two smaller but congruent angles.
Biconditional	A pair of IF/THEN (conditional) statements which are the converse of each other, and both forms are always true. The two conditional statements can then be combined into a single statement with the form ‘If and Only If…(IFF).
Complementary (Angles)	Angles are complementary if their measures added together equal 90º.
Conclusion	A statement (true or false) which is the logical result of a hypothesis.
Conditional	A statement which is true ONLY when one or more other statements are also true. Usually in the form of IF (something is true) THEN (something else is also true).
Conjecture	A conjecture is an idea or statement which is believed to be true, usually because some evidence has been found to support it. A conjecture can become a theorem after it is fully proven.
Converse	The converse of an IF/THEN statement is made by swapping the hypothesis and conclusion. For the original statement p→q, the converse would be q→p. Note: A true statement can often have a false converse!
Counterexample	A specific example which disproves a logical statement. Under the rules of formal logic, a single counterexample is sufficient to make a statement false, regardless of the number of valid examples.
Deductive Reasoning	Deductive Reasoning is the use of logic to derive new conclusions from general ideas or principals. Conclusions reached by correct deduction must be true if the premises or assumptions were true. This is the form of reasoning used most commonly in mathematics. (Compare to inductive reasoning, which only provides conclusions with a high probability of truth.)
Fallacy	A logical error which renders an argument or proof untrue. Even though an argument or proof may seem to be true, a fallacy (or fallacious reasoning) can introduce subtle errors which can be difficult to uncover.
Hypothesis	A statement (true or false) from which a logical conclusion may be made.
Parallel	Lines or planes are parallel if they do not intersect or diverge, no matter how far they are extended.
Perpendicular	Two lines or planes are perpendicular if they meet at a 90º angle.
Proof	The process of establishing a fact with certainty. In math, a proof is a sequence of statements which establish a new fact based on previously known facts and the use of logic. Other fields of study have different forms of proof, often based on evidence rather than logic alone (e.g., law or science). The result of a proof may be considered a theorem.
Q.E.D.	Abbreviation for the Latin saying Quod Erat Demonstrandum; literally meaning “that which was to be proven.” Traditionally used after the last statement of a proof to show that the student had reached the logical goal and completed the assigned proof.
Supplementary (Angles)	Angles are supplementary if their measures added together equal 180º.
Syllogism	A logical statement combing two or more known facts to reach a conclusion. (Example: Since the picture is above the desk, and since the desk is above the floor, therefore the picture is above the floor) .)
Theorem	A statement which has been proven to be correct (see proof). Don’t confuse a theorem in math with a theory in science. A theory (or a conjecture) is a proposed explanation for an observation, but which has not been accepted as proven fact even though there may be a lot of evidence to support the theory. (e.g., Theory of Evolution, Theory of Relativity, etc.)
Vertical Angles	Angles are vertical if they share a common vertex, and the sides of one are lines which also form the sides of the other. Vertical angles are always congruent.

Chapter 3: Parallel Lines and Planes

Alternate Angles	Pairs of angles which lie on opposite sides of a transversal
Concave Polygon	A polygon which is not convex is said to be concave or non-convex. Concave polygons can be recognized by having one vertex angle pointing in toward the interior of the polygon.
Consecutive Angles	Pairs of angles are consecutive if they lie on the same side of a line and no other line or angle is between them.
Convex Polygon	A polygon which has all the internal angles less than 180º. All the points of a convex polygon can be connected using line segments that stay within the boundaries of the polygon.
Corresponding Angles	Corresponding angles are pairs of angles where each angle lies on one of the intersections between a transversal and the crossed lines, and occupy the same relative position at each intersection.
Diagonal	A segment connecting one vertex of a polygon to any non-adjacent vertex.
Exterior Angels	The four angles created by a transversal and lying outside of the two crossed lines.
External Angle	The angle between a side of a polygon and the extension of one the adjacent sides. External angles are always the supplement of the internal angle at any vertex. All the external angles of a polygon will total 360°..
Inductive Reasoning	A form of logical argument which starts with individual examples or observations, and makes general statements by finding a pattern among the observations. Inductive reasoning is commonly used in science and frequently in everyday life. It’s main shortcoming is that results can only be probably true, never certainly true. Sometimes called Abductive reasoning. Compare to Deductive Reasoning
Interior Angles	The four angles created by a transversal and lying between the two crossed lines.
Internal Angle	The angle between two adjacent sides of a polygon, as measured toward the interior of the polygon. The sum of all a polygon’s internal angles will always be a multiple of 180º, according to the formula 180(n-2) for an n-gon.
Parallel Lines	Lines or are parallel when they do not ever intersect or diverge in either direction, and they lie in a single plane (there is one plane that contains both lines). Since they don’t diverge, the distance between the lines is constant no matter where you take the measurement.
Parallel Planes	Two or more planes are parallel if they don’t intersect or diverge. The distance between the planes is always the same (as measured on a line perpendicular to both planes).
Polygon	A geometric figure made up of straight line segments (sides) which are connected (at vertices) to form a closed path. The number of sides is usually referred to with the variable n, hence a generic polygon with n sides is called an n-gon. The most familiar polygons are: triangle (n=3), quadrilateral (n=4; rectangles, rhombi, and squares are special types of quadrilaterals), pentagon (n=5), hexagon (n=6), heptagon (n=7; the correct name is heptagon, not septagon), octagon (n=8), nonagon (n=9, also called the enneagon) decagon (n=10) dodecagon (n=12) … and son on; there are many others named but these are the ones students in my class should be familiar with. Refer to the Wikipedia article on polygons if you want to know what a chiliagon or a triskaidecagon would look like!
Regular Polygon	A polygon with all sides congruent and all angles congruent (a square is the most familiar regular polygon). All regular polygons are both equilateral and equiangular. (They are also cyclic, meaning that they can by inscribed into a circle which includes all the vertices.)
Skew Lines	Lines are skew if they do not intersect AND do not lie in the same plane. Imagine a line draw on a wall, and the path of an arrow that hits the wall in a location not on the line.
Transversal	When two lines are crossed or connected by a third line, the transversal is the third or connecting line. The two crossed lines may be parallel or not.
Triangle	A 3-sided polygon. Because all polygons can be built up from triangles, we pay a lot of attention to them. Triangles are classified according to their internal angles or their side lengths. Classified by Angle: Classified by Side Lengths Equiangular – all angles congruent Equilateral – all sides congruent Isosceles – two angles congruent Isosceles – two sides congruent Obtuse – one angle is greater than 90º Scalene – no pair of sides is congruent Acute – All 3 angles are less than 90º

Chapter 4: Congruent Triangles

Base & Base Angle	In an isosceles triangle, the one side that is not congruent to either of the other two sides is known as the base. The two base angles are at the ends of the base, opposite the legs. Base angles are always congruent in an isosceles triangle.
Congruent	Geometric objects are congruent if they have the same size and shape; distinct from numbers, quantities, or measures which are equal if they have the same size or magnitude. For lines and angles, two figures are congruent if the measure of each (length or degrees) is identical to another line or angle. For more complex figures involving both lines and angles, congruence requires that each line segment or angle of one figure must be congruent to all the corresponding parts of another figure.
CPCT or CPCTC	An acronym (abbreviation) for “corresponding parts of congruent triangles are congruent.”
Hypotenuse	In a right triangle, the longest side is opposite the right angle and is called the hypotenuse. The other two sides are referred to as legs.
Included	In a triangle, any two sides will have one angle between them; this angle is the included angle between the two sides. Similarly, any two angles will have one side between them; this side is included between the two angles. In triangle ABC, Angle A is included by sides AC and AB. Angle C is included by sides AC and BC. Side AB is included by angle A and angle B.
Leg	In an isosceles triangle, the two congruent sides are called the legs (the third side is the base). In a right triangle, the two sides that include the right angle, are called the legs (the third side is the hypotenuse).
Opposite	In a triangle, each vertex is the intersection of two sides; the opposite side is the remote side that doesn’t share any points with that vertex. Similarly, each side has an opposite angle. In triangle ABC, BC is opposite angle A; angle B is opposite side AC. Side AB and angle C are opposites.
Triangle Congruence Postulates	Rules for showing that two triangles are congruent by showing that some of their corresponding parts are congruent. There are four postulates valid for all triangles, and one valid only for right triangles. SSS Triangles are congruent if all of their sides are congruent SAS Triangles are congruent if two sides and the included angle are congruent ASA Triangles are congruent if two angles and the included side are congruent AAS Triangles are congruent if two angles and the non-included side are congruent. HL Two right triangles are congruent if the hypotenuse and one leg are congruent. Note that the combinations AAA and SSA are never sufficient to conclude that triangles are congruent!

Chapter 7: Similarity

Means & Extremes	The first and last terms of a proportion are called the extreme terms, or usually simply ‘the extremes’. The second and third terms of a proportion are called the means. In the proportion , a and d are the extremes; b and d are the means. For any proportional quantities, **the product of the means equals the product of the extremes (ad=bc, usually called cross-multiplying).**
Proportion	An equation stating that two or more ratios are equal, or An extended proportion is a series of equality statements for ratios.
Ratio	A comparison of two quantities their magnitude relative to each other. The ratio of one number to another is the quotient when the first number is divided by the second.
Similarity; Similar Polygons	Polygons or other shapes are similar if they have the same shape but not the same size. In similar figures, all of the corresponding sides or distances will be in the same proportion. (Including the sides, perimeters, and diagonals, but not areas; all the angles will be congruent)
Scale Factor	The ratio of corresponding parts between two similar figures. The number times one figure must grow (or shrink) to match the second.

Chapter 8: Right Triangles

Right Triangle

Any triangle that has one of its angles exactly 90 degrees.

Leg

In a right triangle, one of the sides adjacent to the right angle

Hypotenuse

In a right triangle, the side opposite to the right angle. The hypotenuse is always the longest side of a right triangle.

Geometric Mean

The geometric mean of two numbers is the square root of their product. The number represented by x is the geometric mean of the numbers a and b in this proportion:

Altitude

The segment (or the length of the segment) that joins one vertex of a triangle with the opposite side, and meets the opposite at a right angle.

Pythagorean Theorem

a

Famous theorem that relates the lengths of all three sides of a right triangle. Usually stated as , it is properly applied only if a,b, and c are measures (lengths) of the sides of a right triangle, and c is the hypotenuse.

sine

The sine of an angle in a right triangle is the length of the side opposite the angle divided by length of the hypotenuse.

cosine

The cosine of an angle in a right triangel is the length of the side opposite the angle divided by the length of the hypotenuse.

tangent

The tangent of an angle in a right triangle is the length of the side opposite the angle divided by the length of the adjacent side.

Last updated: January 22, 2008