Chapter 2 Vocabulary - Discovering Geometry

Inductive reasoning

• process of showing that certain statements follow logically from agreed-upon assumptions
• a line intersecting two or more other lines
• the process of observing data, recognizing patterns, and making generalizations about those patters (trial and error)
• a convincing argument that uses deductive reasoning.

conjecture

• A generalization resulting from inductive reasoning.
• A pair of angles formed by a transversal intersecting two lines that lie between the two lines and are on the same side of the transversal.
• A convention for expressing a function rule in terms of its input.
• A rule that, when applied to one set of numbers, generates another set of numbers with at most one output value for each input value.

postulate

• a statement accepted without proof, because it cannot be disproved.
• Two angles formed by a transversal intersecting two lines that lie in the same position relative to the two lines and the transversal.
• A function that has a constant difference between consecutive terms.
• A rule that, when applied to one set of numbers, generates another set of numbers with at most one output value for each input value.

deductive reasoning

• The statement formed by changing the 'if' and 'then' part of a conditional statement.
• process of showing that certain statements follow logically from agreed-upon assumptions
• Two angles formed by a transversal intersecting two lines that lie in the same position relative to the two lines and the transversal.
• A convention for expressing a function rule in terms of its input.

mathematical models

• A rule that, when applied to one set of numbers, generates another set of numbers with at most one output value for each input value.
• A pair of angles formed by a transversal intersecting two lines that lie between the two lines and are on the same side of the transversal.
• A mathematical way of representing a real-world situation, such as a geographic figure, graph, table, or equation.
• A pair of angles formed by a transversal intersecting two lines that do not lie between the two lines and are on opposite sides of the transversal.

converse

• the process of observing data, recognizing patterns, and making generalizations about those patters (trial and error)
• A pair of angles formed by a transversal intersecting two lines that lie between the two lines and are on the same side of the transversal.
• a convincing argument that uses deductive reasoning.
• The statement formed by changing the 'if' and 'then' part of a conditional statement.

transversal

• a conjecture that is proven
• a line intersecting two or more other lines
• A pair of angles formed by a transversal intersecting two lines, that lie between the two lines and are on opposite sides of the transversal.
• The statement formed by changing the 'if' and 'then' part of a conditional statement.

corresponding angles

• The ratio rise/run.
• a proof that has the statement in one column and the reason in another column
• A mathematical way of representing a real-world situation, such as a geographic figure, graph, table, or equation.
• Two angles formed by a transversal intersecting two lines that lie in the same position relative to the two lines and the transversal.

Alternate interior angles

• a proof that has the statement in one column and the reason in another column
• A pair of angles formed by a transversal intersecting two lines, that lie between the two lines and are on opposite sides of the transversal.
• A function that has a constant difference between consecutive terms.
• The statement formed by changing the 'if' and 'then' part of a conditional statement.

Alternate exterior angles

• A mathematical way of representing a real-world situation, such as a geographic figure, graph, table, or equation.
• A pair of angles formed by a transversal intersecting two lines, that lie between the two lines and are on opposite sides of the transversal.
• process of showing that certain statements follow logically from agreed-upon assumptions
• A pair of angles formed by a transversal intersecting two lines that do not lie between the two lines and are on opposite sides of the transversal.