Geometric Reasoning

In this topic, I learned how to easily identify biconditional statements and their conditionals and converse. I also learned what makes a definition a good one.

Biconditional Statements

 

(Biconditional) A statement is a biconditional statement if and only if it's two conditionals in the form "p if and only if q."

(Conditional) If a statement is biconditional, then it is two conditionals in the form "p if and only if q."

(Converse) If a statement is two conditionals in the form "p if and only if q," then it is biconditional.

Angle Bisector

Definition: a line that divides an angle into two equal parts

A definition is good if it reversible and can be written as a true biconditional:
A line is an angle bisector if and only if it divides an angle into two equal parts.

Traffic Ticket

You will get a traffic ticket if and only if you are speeding.

1)If you get a traffic ticket, then you are speeding.(false)

2) If you are speeding, then you will get a traffic ticket.(true)

The biconditional is false because there are numerous other reasons for receiving a traffic ticket such as driving under the influence, cell phone usage, or violating a car registration/ driver's license requirement. 

In conclusion, you can identify a biconditional statement using two conditionals. Also, if you want to know if a definition is a good definition it has to be reversible and can be written as a true biconditional.