If a + b = 15 and a + b + c = 15 + c which axiom of Euclid does the statement illustrate ?

Answer

To solve the question, we need to analyze the given statements and identify which of Euclid's axioms they illustrate.

**Step 1: Understand the given equations.**
We have two equations:
1. \( a + b = 15 \)
2. \( a + b + c = 15 + c \)

**Step 2: Analyze the first equation.**
The first equation states that the sum of \( a \) and \( b \) equals 15.

**Step 3: Analyze the second equation.**
The second equation can be interpreted as adding \( c \) to both sides of the first equation. If we take the first equation \( a + b = 15 \) and add \( c \) to both sides, we get:
\[ a + b + c = 15 + c \]

**Step 4: Identify the axiom being illustrated.**
According to Euclid's axioms, specifically Axiom 2, it states that "if equals are added to equals, the wholes are equal." In our case, since we added \( c \) (which is equal on both sides) to both sides of the equation \( a + b = 15 \), we maintain equality, thus illustrating this axiom.

**Conclusion:**
The statement illustrates Euclid's Axiom 2: "If equals are added to equals, the wholes are equal."

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