Chapter 10

Chapter 10

Logical Thinking and Properties​

Some text here about the topic of discussion

Definitions:

Perpendicular Bisector: A perpendicular bisector is a line segment ​that cuts another line segment in half and intersects at a 90 degree angle.

​Angle Bisector: An angle bisector is a ray that cuts an angle in half.

​Logical Sequence: A logical sequence is a sequence where you can predict what the next term will be based on a pattern.

​Counter Example: A counter example is an example that proves an argument (or statement) false.

​

Subject | Subject

Some text here about the topic of discussion

More Definitions:

Hypothesis: An unproven statement that is usually followed by a supporting fact.

​Conclusion: In an "if, then" statement, the conclusion follows the "then".

"If a garden has flowers, then it is pretty."

Converse: The converse is found by switching the hypothesis and conclusion of a statement.​

​Inverse: The inverse comes from negating the hypothesis and conclusion. "If not ...., then not ...."

Contrapositive: The contrapositive comes from switching the conclusion and hypothesis and negating them.​

​A. If a square has length 10 in, then it has area 100 in ².

​

​

​B. If someone has a LHS shirt on, then the shirt they are wearing is cool.​

​

​

C. ​If a rectangle has length 5, then it has area 25.

​

​

​

​

​Consider the following statements:

How to draw conclusions:

​A. All good football players can tackle. Tyler is a good football player.

​

​

B. ​If you do not practice you will not be good at sports. If you aren't good at sports you won't get a college scholarship.

​

​

C. ​Break the statement into two conditional statements:

​A line is parallel to another line if and only if the two lines never intersect.

​

Various Properties:

Properties of Equality: The properties of equality tell us that whatever we do on one side of the equation we also have to do on the other side of the equation. They are the; Addition, Subtraction, Multiplication and Division Properties of Equality.

​

Transitive: Transitive basically means things transfer. If A implies B and B implies C, then A implies C.

If line A is equal to line B and line B is 5 cm long, then line A is 5 cm long.​

If Wyatt and Trevor are the same age and Trevor is 16 years old, how old is Wyatt?​

Subject | Subject

Some text here about the topic of discussion

Various Angle Theorems:

​Vertical Angles: When two lines intersect, the angles across from each other are equal.

​

​

Supplementary Angles: When angles combine to form a straight line, they sum to 180 degrees.

​

​

​

​

Subject | Subject

Some text here about the topic of discussion

​Ex: Solve for x

​Ex: Construct the angle bisector of the angle.

​Ex: Construct the perpendicular bisector of the line segment.