VOCABULARY
CONDITIONALS AND BICONDITIONALS
DEDUCTIVE REASONING
REASONING IN ALGEBRA AND GEOMETRY
PROVING ANGLES CONGRUENT
100
An if-then statement.
What is a conditional statement
100
Q -->P
What is the Converse of a conditional statement.
100
If p-->q is true and p is true, then q is true.
What is the Law of Detachment.
100
If a=b, then b=a.
What is Symmetric property of equality.
100
A statement that you prove.
What is a theorem.
200
A single true statement that combines a true conditional and its true converse.
What is a biconditional
200
~Q-->~P
What is the contrapositive.
200
If p-->q and q-->r is true, the p-->r is true.
What is The Law of Syllogism.
200
If a=b, then b can replace a in any expression.
What is Substitution property of Equality.
200
All right angles are congruent.
What is the congruent complements theorem.
300
Sometimes called logical reasoning, is the process of reasoning logically from given statements or facts to a conclusion.
What is Deductive Reasoning.
300
This is the converse of the statement: If you play the tuba, then you play an instrument.
What is If you play an instrument, then you play the tuba.
300
The conclusion you make from the following statements: If you practice tennis everyday, then you will become a better tennis player. Arthur practices tennis everyday.
What is Arthur will become a better player.
300
The property that justifies going from the first statement to the second. 3(x+5)=9 3x+15=9
What is Distributive Property
300
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.
What is the congruent supplements theorem.
400
If a=b and b=c, then a=c
What is Transitive Property.
400
The biconditional of the statements: If a figure is a hexagon, then it is a polygon with exactly 6 sides. If a figure is a polygon with exactly 6 sides, then it is a hexagon.
What is A figure is a hexagon if and only if it is a polygon with exactly 6 sides.
400
The conclusion you get from the following statements: If your father buys new gardening gloves, then he will work in his garden. If he works in his garden, then he will plant tomatoes.
What is If your father buys new gardening gloves, then he will plant tomatoes.
400
(1/4)x=7 x=28
What is the multiplication Property.
400
(x+10) and (4x-35) are vertical angles. Solve for X and the two angles
What is x=15 (x+10)=25 (4x-35)=25
500
A convincing Argument that uses deductive reasoning.
What is a Proof.
500
The conditional and converse to the true biconditional statement: Two angles are complementary if and only if the sum of their measures is 90.
What is If two angles are complementary, then the sum of their measures is 90. If the sum of the measures of two angles is 90, then the angles are complementary.
500
The conclusion you get from the following true statements: If you live in Accra, then you live in Ghana. If you live in Ghana, then you live in Africa. Hailey lives in Accra.
What is Hailey lives in Africa.
500
The reasoning for the following statements. Given: 5x+1=21 Prove:x=4 5x+1=21 5x=20 x=4
What are Given Subtraction property Division Property
500
You are given 3 angles. 4y and (x+y+10) are vertical angles. 2x and (x+y+10) are supplementary. Find the value of each variable and the measure of each angle.
What is x=50 y=20 4y=80 2x=100 (x+y+10)=80
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