Geometry Reasoning and Proof
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What is a conjecture?
An unproven statement based on observations. The conclusion that you draw.
What is a counter example?
A specific example that disproves a theory. For example, to disprove the fact that all subtractions end in a postive number, 7-9=-2 is a counter example.
What is a conditional statement?
A statement with a hypothesis and a conclusion, or an if-then statement.
What is an inversion?
A negation of the statement, or making it opposite. Positive staements become negative and positive statements become positive. You must negate both parts of the statement.
What is the converse of a statement?
To flip it. The if becomes the then and the then becomes the if. You do flips in coverse shoes.
What is contrapositive?
To flip and negate the statement. It is also logically equivalent and is true.
What are equivalent statements?
Statements that are both false, or that are both true. They mean the same thing. A contrapositive always results in an equivalent statement.
What are perpindicular lines?
Two lines that form right angles. Or two angles that form right angles are perpindicular.
What is a biconditional statement?
A statement that has if and only if in the middle. It is a conditional statement that is true in its regular form and in its converse form.
What is deductive reasoning?
Using facts and properties of logic to form a logical argument.
What is the law of Detachment?
If you know a statement that is true, and then you are given a hypothesis is also true, then the conclusion will be true also.
What is the Law of Syllogism, or the chain rule?
- Words like below, as long as the first two stements are true.
- If a happens, b happens.
- If b happens, c happens.
- Therefore, if a happens, c happens.
Based on postulate 5, how many lines are there between 2 points?
There is one line.
Based on postulate 6, how many points does a line consist of?
At least 2
Based on postulate 7 how many intersections are posible between 2 intersecting lines?
Based on postulate 8, How many planes are there in 3 non collinear points?
There is one plane
Based on postulate 9, how many points does a plane consist of?
At least 3 non collinear points
Based on postulate 10, what plane is the line that connects two points on a plane in?
The same plane
Based on postulate 11, what is the intersection point of two planes that intersect?
What do you know about lines that are perpindicular to planes?
Lines that are perpindicular to planes must be perpindicular to every line in the plane that crosses that one point.
What is the addition property of equality?
Adding. A=B, so A+C=B+C
What is the subtraction property of equality?
Subtracting. A=B, A-C=B-C
What is the multiplication property of equality?
Multiplying. A=B, so AC=BC
What is the division property?
Dividing. A=B so A/C=B/C
What is the substitution property?
Substituting things in. a=b, so any a can be changed to a b and any b can be changed to an a
What is the reflexive property?
When something is equal to itself, whether it be a number, a segment, or an angle.
What is the symmetric property of equality?
It is when you change the sides of things, whether it is a number, segment, or angle. A=B, so B=A
What do you know about vertical angles?
Vertical angles are congruent.
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