Reasoning
An educated guess or a theorem that is yet to be proven.
What is a CONJECTURE?
A mathematical statement assumed to be true.
What is a POSTULATE?
Two angles with a common side and a common vertex but with no common points in their interiors.
What are ADJACENT ANGLES?
a(b + c) = ab + ac
What is the DISTRIBUTIVE PROPERTY?
If x - 14 = 27, then x = _____.
What is 41 ?
A type of reasoning that starts from observation and moves from one or more specific observations to a general conclusion.
What is a INDUCTIVE REASONING?
A mathematical statement that has been or is to be proved on the basis of established definitions and properties.
What is a THEOREM?
Non-adjacent angles formed by intersecting lines. These angles are always congruent.
What are VERTICAL ANGLES?
(Vertical Angles Theorem: If two angles form a pair of vertical angles, then they are congruent.)
If a = b, then a + c = b + c.
What is the ADDITION PROPERTY OF EQUALITY?
If t + 2.5 = -14, then t = _____.
What is -16.5 ?
An example that shows a statement is not always true.
What is a COUNTEREXAMPLE?
A clear, logical structure of reasoning that begins from accepted ideas and proceeds through logic to reach a conclusion.
What is a PROOF?
Two angles that have a common side and whose other sides point in opposite directions.
What is a LINEAR PAIR?
(Linear Pair Postulate: If two angles form a linear pair, then they are supplementary angles.)
If a = b and b = c, then a = c.
What is the TRANSITIVE PROPERTY OF EQUALITY?
If 3m - 2 - m = -18, then m = _____.
What is -8 ?
A statement in the form if p, then q in which the hypothesis (the if part) implies the conclusion (the then part).
What is a CONDITIONAL STATEMENT?
A geometric reasoning proof that graphically represents a logical flow and shows statements and conclusions connected with arrows.
What is a FLOWCHART PROOF?
The sum of the measures of a pair of complementary angles is _____.
What is a 90 degrees?
If a = b, then ac = bc.
What is the MULTIPLICATION PROPERTY OF EQUALITY?
If 3(2x + 1) = x - 7, then x = _____.
What is -2 ?
A type of reasoning that uses previously proven or accepted properties to reach conclusions
What is DEDUCTIVE REASONING?
A proof shown in two columns. The first column shows the steps, and the second column shows the justification for each step.
What is a TWO-COLUMN PROOF?
The sum of the measures of a pair of supplementary angles is _____.
What is 180 degrees?
5x + 6 = 5x + 6
What is the REFLEXIVE PROPERTY OF EQUALITY?
If (3x + 5)/4 = 8, then x = _____.
What is 9 ?