Conditional Statements
What is the converse of:
If it is cold, then it is snowing.
What is...
If it is snowing, then it is cold.
What property says...
if a=b and b=c, then a=c.
What is...
Transitive Property.
A process that includes looking for patterns and making conjectures based on those patterns.
What is....
Inductive Reasoning
Decide if the following statement is true always, sometimes, or never.
Two angles that are vertical are nonadjecent.
What is...
always.
What does the Vertical Angle Theorem state?
What is...
If two angles are vertical angles, then they are congruent.
Construct a conditional statement from the given.
I studied for 3 hours and I got an A on the test.
What is...
If I study for 3 hours, then I will get an A on the test.
Choose the property that justifies the following.
-3x+5+2x=12 and x=4
-3(4)+5+2x=12
What is...
Substitution Property.
An educated guess based on known information is a...
What is....
Conjecture.
Decide if the following statement is true always, sometimes, or never.
If two angles form a linear pair, then they are supplementary angles.
What is...
always. This is the Supplement Theorem.
What does the Segment Addition Postulate state?
What is...
If B is between A and C, then AB + BC = AC.
OR
If AB + BC = AC, then B is between A and C.
Construct an inverse from the given conditional statement...
If it is a ripe banana, then it is yellow.
What is...
If it is not a ripe banana, then it is not yellow.
What property justifies the following statement...
If AB=CD and CD=EF, then AB=EF.
What is...
Transitive Property.
A convenient method for organizing the truth values of statements...
What is...
a truth table.
Decide is the following statement is true always, sometimes, or never.
A line contains 3 or more points.
What is...
sometimes.
Make a conjecture given that BD is an angle bisector of angle ABC.
What is...
angle ABD is equal in measure to angle CBD.
What type of related conditional statement is the statement formed by negating the converse of the conditional statement?
What is...
Contrapositive Statement.
What property justifies the following...
3 (4x + 1) = 15
12x + 3 = 15
What is...
Distributive Property.
A law that states If p, then q is a true conditional and p is true, then q is also true.
What is...
Law of Detachment
Decide if this statement is true always, sometimes, or never.
Two angles that form a linear pair are congruent...
What is...
sometimes.
Use the Law of Syllogism to write a valid conclusion.
(1) If you like strawberries, then you like fruit.
(2) If you like fruit, then you are healthy.
What is...
(3) If you like strawberries, then you are healthy.
Construct a contrapositive for the following statement...
I went to the dentist, so I do not get cavities.
What is...
If I get cavities, then I did not go to the dentist.
What is the next statement and reason in this proof?
1/2 (2x) + 3 = 1/2 (8) Multiplication Property
What is...
x + 3 = 4 Simplification
Joining a conditional statement and its converse using the words 'if and only if'...
What is...
Biconditional Statement.
Complete the proof.
Given: AC=BD
Prove: AB is congruent to CD
(** Draw an image where you have a line with points A, B, C, D in this order**)
AC=BD Given
AB+BC=AC; BC+CD=BD Segment Addition Post.
AB+BC=BC+CD Substitution
AB=CD Subtraction
AB is congruent to CD Def. of Congruence
Can you use the Law of Detachment to make a valid conclusion? Write valid or invalid. If you can make a valid conclusion, what is that conclusion?
(1) If two angles are supplementary, then the sum of the measures is 180.
(2) angles 1 and 2 are supplementary.
What is...
Valid.
The sum of angles 1 and 2 measures 180.