LOGIC & REASONING
This type of reasoning uses specific examples to form a general conclusion.
What is inductive reasoning?
Two lines that intersect to form right angles are called this.
What are perpendicular lines?
This type of proof is organized in two columns: statements and reasons.
What is a two-column (formal) proof?
A line that intersects two or more lines at different points is called this.
What is a transversal?
Two angles that share a common vertex and side but no interior points are called this.
What are adjacent angles?
This type of reasoning starts with general statements to reach a specific conclusion.
What is deductive reasoning?
This postulate states that through any two points there is exactly one line.
What is the Two-Point Postulate?
The reason used when a statement follows directly from the given information.
What is 'Given'?
These angles are on the same side of the transversal and in the same position at each intersection.
What are corresponding angles?
Two angles whose measures sum to 90° are called this.
What are complementary angles?
A statement written in 'if-then' form is called this.
What is a conditional statement?
A point, line, or plane that divides a segment into two congruent segments is called this.
What is a midpoint (or segment bisector)?
The property that states a = a (any quantity equals itself).
What is the Reflexive Property?
hen parallel lines are cut by a transversal, these angle pairs on opposite sides of the transversal between the parallel lines are congruent.
What are alternate interior angles?
Two angles formed by two intersecting lines that are across from each other; they are always congruent.
What are vertical angles?
The negation of the hypothesis and conclusion of a conditional statement, in reverse order.
What is the contrapositive?
This theorem states that if two angles are supplementary to the same angle, then they are congruent to each other.
What is the Congruent Supplements Theorem?
The property that allows you to substitute one equal quantity for another in an equation or statement.
What is the Substitution Property?
When parallel lines are cut by a transversal, co-interior (same-side interior) angles are this.
What are supplementary angles (sum to 180°)?
An exterior angle of a triangle equals the sum of these two angles.
What are the two non-adjacent interior angles (remote interior angles)?
If a conditional statement and its converse are both true, they can be combined into this type of statement using 'if and only if.
What is a biconditional statement?
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines must be this.
What are parallel lines?
A proof method that assumes the opposite of what you want to prove, then shows a contradiction arises.
What is an indirect proof (proof by contradiction)?
f two lines are both perpendicular to a third line, you can conclude this about the two lines.
What is that they are parallel to each other?
The Angle Addition Postulate states that if D is in the interior of angle ABC, then m∠ABD + m∠DBC equals this.
What is m∠ABC?