Geometry Ch. 2 of Prentice Hallconditionals, biconditionalscounter examples
Biconditional
Conditional
Converse
Counterexample
Yes, it is an accurate definition.
No, it is not an accurate definition.
Two angles are adjacent if and only if they share a common side.
A point is the midpoint of a segment if and only if it is between the endpoints of the segment.
Two angles are supplementary if and only if they form a linear pair.
Two lines are parallel if and only if they never intersect.
D is the midpoint of Segment CE.
D is the midpoint of Segment AB.
Segment AB is perpendicular to Segment CE.
Segment AB has the same length as Segment CE.
If p → q and q → r are true statements, then p → r is a true statement.
If p → q is a true statement and p is true, then q is true.
If p → q is a false statement and p is false, then q is false.
If p → q and q → r are false statements, then p → r is a false statement.
Addition Property
Reflexive Property
Substitution Property
Transitive Property
M∠AEB = 83
M∠BEC = 97
∠AEB and m∠DEC are congruent angles.
# ∠BEC and m∠CED are vertical angles.
∠AOC
∠BOC
∠AOE
∠DOE
Adjacent angles; vertical angles
Vertical angles; adjacent angles
Adjacent angles; complementary angles
Vertical angles; supplementary angles
Symmetric Property
Substitution Property
Multiplication Property
Reflexive Property
I do not have room for dessert.
I did not finish my dinner.
I had macaroni and cheese for dinner.
No conclusion possible
14
10
7
2
Janina is shortest.
Janina is taller than Isabel.
Franz is the tallest.
Ellen is shorter than Isabel.