2.1 If-Then Statements3 - Parallel lines
2.2 How To Prove        Theorems
2.3 Pairs Of Angles
2.4 Perpendicular Lines
5.1 Parallelograms6 - Inequalities
5.2 Parallel lines       Theorem
5.3 Special        Parallelograms
6.1 Inequalities7 - Similar Polygon
6.2 Inequalities In A       Triangle
6.3 Inequalities In 2       Triangles
10.1 Construction11 - Areas of 2D objects
10.2 Perpendicular Lines
10.3 Parallel Lines
10.4 Concurrent Lines
11. 1 Areas Of          Polygons12 - Areas and Volumes
11. 2 Circles and          Similar Figures
12.1 Prisms13 - Coordinates
12.3 Cylinders and          cones
12.5 Similar solids
13.1 Geometry and          Algebra14 - Reflection/Rotation
13.2 Lines and          Coordinates
• Understand If-Then Statements; Conditionals, Biconditional, Converse, Counterexample, Inverse, and Contrapositives.
Know most of the properties from Algebra
2-1 If-Then Statements:
If-Then Statements: An if-then statement is just what the name says it is. It is a statement that proves if something happens then something else will happen. For example,
Chris went to the store after school, then he will buy something.”
D is between C and E, then CD + DE = CE”
These kinds of if-then statements are called conditional statements, or just conditionals.
To symbolize an if-then statement, then let p represent the hypothesis, and q represent the conclusion.
If p, then q.
Switching the hypothesis and the conclusion forms a converse of a conditional.
Statement: If p, then q. Converse If q, then p.
A statement and a converse say different things. Some converses come out to be false while the statement is true. For example,
“If Chris lived in California, then he lives East of the capital of
“If Chris lives East of the capital of the USA, then he lives in California”
As anyone can see, the converse is false. If Chris lives east of the capital, there are a number of states he could live in, not just California. In cases such as these, where the hypothesis (p) is true and the converse (q) is false, there is a name. The names of these cases are called counterexample.
Conditional statesmen are not always written with the ‘if’ clause first. For example,
The inverse is simply the
conditional with ‘not’ added to it.
An inverse but switched around with the p and q. For example,
Statement: If p, then q
Inverse: If not p, then not q
Contrapositive: if not q, then not p
statement is always true with the contrapositive, but a statement
is not logically equivalent to its converse or to its inverse.
Properties from Algebra:
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