Vocabulary for week of 9/21

Monday 9/17

Paragraph Proofs – A kind of proof in which the steps are written out in complete sentences, in paragraph form. Identical in content, but different in form.

Counterexample – A counterexample is an exception to a proposed general rule. An example which disproves a proposition. For example, the prime number 2 is a counterexample to the statement “All prime numbers are odd.

Conditional statement – A statement that can be expressed as an if-then statement. For example, “If a polygon is a hexagon, then it has exactly six sides.

Deductive Structure – A system of thought in which conclusions are justified by means of previously assumed or proved statements.

Postulate – Something assumed without proof. A proposition that is accepted as true.

Definition – A statement expressing the essential nature or meaning of a term or idea.

Hypothesis – A tentative assumption made in order to draw out and test its logical consequences.

Conclusion – The “then” clause in a conditional statement.

Converse – A statement associated with a conditional statement. Statement “If p, then q.” The converse is “If q then p.” To write a converse you reverse the part after the “IF” with the part after the “THEN”.

Inverse – A statement associated with a conditional statement. A conditional resulting from negating the antecedent and consequent of the original conditional.
EX: Original conditional: If a quadrilateral is a square, then it is a rectangle.

Inverse: If a quadrilateral is not a square, then it is not a rectangle.
NOTE: Sometimes the original conditional will be true, but its inverse will be false.

Contrapositive – A conditional resulting from negating and switching the antecedent and consequent of the original conditional.
Original statement “If you live Wyckoff, then you live in New Jersey.” The contrapositive  is “If  you don’t live in New Jersey,  then you don’t live in Wyckoff.”

Vocabulary for week of 9/14

Monday 9/10

Collinear – Points are collinear if they lie on the same line. Collinear points lie along a straight line.

NonCollinear – Points that do not line on the same line, typically dealing with three or more points.

Theorem – A mathematical statement that can be proved to be true.

Two column proof – A deductive argument that contains statements and reasons
organized in two columns. A kind of proof in which the statements (conclusions) are listed in one column, and the reasons for each statement’s truth are listed in another column.

Bisect – To cut something (such as a line segment or an angle) into two equal parts.

Midpoint – A point on a line segment that divides the segment into two congruent segments.

Bisector – A ray whose end point is the vertex of the angle and which divides the angle into two equal angles. – Example

Trisect – To cut something (such as a line segment or an angle) into three equal parts.

Trisection points – Two points on a line segment that divides a segment into three congruent segments. The two points at which the segment is divided are called the trisection points of the segment.

Trisector – Two rays that divide an angle into three congruent angles trisect the angle. The dividing rays are called the trisectors of the angle.

Vocabulary for week of 9/08

Friday 9/7

Degree – A common unit of measurement used to determine the size of an angle.

Acute Angle – An angle that measures more than 0° and less than 90°.

Right Angle – An angle that measures exactly 90°.

Obtuse Angle – An angle that measures more than 90° and less than 180°.

Straight Angle – An angle that measures exactly 180°. A straight angle appears as a straight line.

Parts of a Degree
Minutes – each degree is divided into 60 minutes (like an hour)
Seconds – each minute is divided into 60 seconds
60’ = 1° → 60 minutes = 1 degree
60” = 1’ → 60 seconds = 1 minute

27.5° = 27° 5’
45° = 44° 60’

Congruent – Two objects are congruent if they have the same dimensions and shape. Very loosely, you can think of it as meaning ‘equal’. The symbols is .

Congruent angles - Angles are congruent if they have the same angle measure in degrees. –> Example

Congruent line segments - Line segments are congruent if they have the same length. –> Example

THURSDAY 9/06

Point – A point is an exact location. A point is just like a dot. Points are zero-dimensional. That basically means that they have no height, length, or width. They are just there.
Lines – A two-dimensional object that has no endpoints and continues on forever in a plane; formed of infinite points.
Number line – A two-dimensional object that has no endpoints and continues on forever in a plane; formed of infinite points.
Line Segment - is a part of a line that is bounded by two end points, which have a finite length, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square
Endpoints – A single point indicating where a line segment or ray ends. A ray has one endpoint, and a line segment has two endpoints.
Ray – A series of points that extends endlessly in one direction. A ray has one endpoint, but its length cannot be measured. The endpoint must be named first.
Angle - A shape formed by two rays sharing a common endpoint or two lines that intersect. An angle has one vertex and two sides.
Vertex – The point of an angle where its two sides meet.