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It is known that if x+y=10, then x+y+z=1...

It is known that if `x+y=10`, then `x+y+z=10+z`. The Euclid's axiom that illustrates this statement is

A

first axiom

B

second axiom

C

third axiom

D

fourth axiom

Text Solution

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The correct Answer is:
To solve the question, we need to identify which of Euclid's axioms illustrates the statement: "if \( x + y = 10 \), then \( x + y + z = 10 + z \)". ### Step-by-Step Solution: 1. **Understanding the Given Statement**: We start with the equation \( x + y = 10 \). This is our initial condition. 2. **Adding the Same Quantity to Both Sides**: We then add \( z \) to both sides of the equation: \[ x + y + z = 10 + z \] 3. **Identifying the Axiom Used**: The operation we performed (adding \( z \) to both sides of the equation) is a fundamental property of equality. According to Euclid's axioms, this corresponds to the second axiom, which states: "If equals are added to equals, the wholes are equal." 4. **Conclusion**: Therefore, the Euclid's axiom that illustrates the statement is the **second axiom**. ### Final Answer: The correct option is the **second axiom**. ---
To solve the question, we need to identify which of Euclid's axioms illustrates the statement: "if \( x + y = 10 \), then \( x + y + z = 10 + z \)". ### Step-by-Step Solution: 1. **Understanding the Given Statement**: We start with the equation \( x + y = 10 \). This is our initial condition. 2. **Adding the Same Quantity to Both Sides**: ...
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