What is the law of syllogism in geometry?

In geometry, the law of syllogism is a principle that states that if a conditional statement is true and its conclusion is used as the hypothesis for another conditional statement, then the conclusion drawn from the second conditional statement must also be true.

For example, if we have the following conditional statements:

1. If A, then B
2. If B, then C

According to the law of syllogism, we can conclude: If A, then C

This principle is often used in geometric proofs to establish logical connections between different statements and to draw conclusions based on established facts. It helps to build a chain of reasoning to prove theorems and solve geometric problems.