# What Is the Law of Syllogism in Geometry?

**The law of syllogism in geometry states that "if p, then q," and "if q then r."** It’s also possible to derive a third statement that "if p, then r." The “if-then” statement applies to the law of syllogism to aid in deductive reasoning.

For example, if Jane encounters a traffic jam today, she reports to work late, and if Jane reports to work late, her boss penalizes her. Letting "p" be the statement “encounters a traffic jam today,” "q" be the statement “reports to work late” and "r" be the statement “her boss penalizes her,” by the law of syllogism, a third statement may be deduced that if Jane encounters a traffic jam today, her boss will penalize her.

The relationship between "p" and "q," which is p ? q and read as "if p, then q," is called a conditional statement and involves a hypothesis that’s followed by a conclusion. For example, if 50 percent of students in a class is male, then 50 percent of the class must be female. Interchanging positions of the hypothesis and its conclusion result in the converse statement: if 50 percent of students in a class is female, then 50 percent of the class must be male. A conditional statement and its converse don’t have the same implications.