Things which are equal to the same thing are _____to one another

Options

A. Perpendicular
B. Not equal
C. Equal
D. Parallel

Answer

To solve the question "Things which are equal to the same thing are _____ to one another," we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Statement**: The question is asking us to fill in the blank based on a fundamental property in geometry, specifically related to equality.

2. **Referencing Euclid's First Axiom**: The statement resembles Euclid's first axiom, which states: "Things which are equal to the same thing are equal to one another." This means if two things are both equal to a third thing, then they must be equal to each other.

3. **Identifying the Options**: The options provided are:
- Perpendicular
- Not equal
- Equal
- Parallel

4. **Applying the Axiom**: According to Euclid's first axiom, if we have two things, say A and C, that are both equal to a third thing B, then A must be equal to C.

5. **Filling in the Blank**: Since the statement we are analyzing is directly derived from Euclid's axiom, we can conclude that the correct term to fill in the blank is "equal."

6. **Final Answer**: Therefore, the complete statement is: "Things which are equal to the same thing are equal to one another."