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A _________________is an unproven statement that is based on observation or given
information.
To show a conjecture is true, you must show it is true for _______________________.
To show a conjecture is false, you must provide only one _______________________.
Ex 1: Given: 1 and 2 are supplementary
Conjecture: 1 and 2 form a linear pair
Ex 2: Given: 1 and 2 form a linear pair
Conjecture: 1 and 2 are supplementary
A ________________________is a logical statement that has two parts: If….then…
The _________________ is the “if” part.
The _________________ is the “then” part.
Ex 3: Write the following statements as conditional statements.
a. Two angles that form a linear pair are supplementary.
b. All 90 angles are right angles
The ________________of a conditional statement switches the hypothesis and the conclusion.
The second answer we wrote for example 3b is the _____________of the first answer.
The _______________ of a conditional statement negates both the hypothesis and the
conclusion.
Ex 4: Write the inverse of the following and state whether it is a true statement.
a. If two lines form a linear pair, then they are supplementary.
b. If an angles is a right angle, then it measures 90 .
The _______________________of a conditional statement takes the _______________ of the
________________.
Ex 5: If an angle is a right angle, the it measures 90 .
Converse:
Contrapositive (inverse of the converse):
If a conditional statement and its converse are both true, then we can write it as a ___________
statement by using the words “if and only if.” Any valid definition can be written as a _______________________.
Ex 6: If an angles is a right angle, then it measures 90 .
Biconditional statement:
Ex7:
Perpendicular line intersect to form right angles.
Conditional statement:
Converse:
Inverse:
Contrapositive:
Biconditional:
If the _______________of a true conditional statement is true, then the _________________ is
also true. This is called a direct argument or the Law of Detachment.
Ex 8: If two segments have the same length, then they are congruent. You know BC = XY .
Ex 9: If two angles form a linear pair, then they are supplementary. You know
linear pair.
Law of Syllagism:
If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
If hypothesis p, then conclusion r.
If these are true,
then this is true.
Ex 10: If two angles form a linear pair, then they are supplementary.
If two angles are supplementary, then their sum is 180 .
P. 82 (1, 2, 4, 7, 10-12, 16-21)
p. 90 (4, 7, 12)
1 and
2 are a