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Types of proofs
Parts of a proof
Proof examples
Properties
Theorems
100
A single truth statement that combines the true and its converse.
What is a bioconitional statement?
100
The part p following if.
What is a hypothesis?
100
If a student gets an A on their midterm, then they will pass their exam. Michaela gets an A on her midterm, she will pass her class.
What is the law of detachment?
100
A = A
What is the Reflective Property?
100
A conjecture or statement you prove true.
What is the definition of a theorem?
200
The process of reasoning logically from given statements or facts to a conclusion.
What is deductive reasoning?
200
Part q following then.
What is a conclusion?
200
If it is Christmas, you need to go shopping. If you need to go shopping, you have to spend money. If it is Christmas -> you need to spend money.
What is the law of sllyogism?
200
A=B, then B=A.
What is the symmetrical property?
200
If triangle ABC is a right triangle, with angle B being a right angle, and if triangle DEF, is also a right triangle,with angle E also being a right angle. From this information we can conclude that angle B is congruent to angle E, why is this so?
Angle B is congruent to angle E,because all right angles are congruent
300
The process for reasoning based on patterns you observed.
What is inductive reasoning?
300
An if then statement.
What is a conditional statement?
300
If you live in Massachusetts, then you live in the United States. If you live in the United States you are in North America. Henry lives in Massachusetts -> he lives in North America.
What is the law of syllogism and the law of detachment?
300
If A=B and B=C, then A=C.
What is the Transitive Property?
300
Triangle ABC has a perpendicular bisector, CD, if angle ACD is congruent and supplementary to angle DCB, what can conclude from this information?
We can conclude that angles ACD and DCB are both right angles.
400
Something that has the same truth value.
What is Equivalent Statement?
400
The opposite of a statement?
What is negation?
400
A triangle is complementary iff it is 90 degrees.
What is a biconditional statement?
400
If a=b, then b can replace a in any expression.
What is the Substiution Property?
400
If angle 1 is a complement and to angle 2, and angle 2 is a complement to angle 3, then what is the relation between angles 1 and 3. Please explain why.
Angle 1 is congruent to angle 3, because, if two angles are complements of the same angle, or of congruent angles, then the two angles are congruent.
500
It allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement.
What is Law of Syllogism?
500
The convincing argument that uses deductive reasoning. It logically shows how conjecture is true.
What is a proof?
500
Write your own proof using at least five steps! DAILY DOUBLE!
What is... (answers vary)?
500
The Properties of Congruence.
What is the Reflexive. Symmetric, and Transitive Properties?
500
If angle 1 and angle 3 are supplements, and angle 2 and angle 3 are supplements, what is concluded based on the information, given in terms of the relationship between angles 1 and 2. Please explain why.
angle 1 is congruent to angle 2. This because two angles that are supplements of the same, or congruent angles, are congruent to each other.