Name the property of equality that justifies that statement
"If m<1 + m<2 = m<3 + m<4 and m<2 = m<4, then M<1 + m<4 = m<3 + m<4"
A. Subtraction
B. Transitive
C. Symmetric
D. Substitution
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Subtraction
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Reflexive property
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The property of equality that justifies the given statement is D. Substitution.
To understand why, let's break down the given statement:
1. "If m<1 + m<2 = m<3 + m<4 and m<2 = m<4"
2. We have the equality "m<1 + m<2 = m<3 + m<4" and we also know that "m<2 = m<4".
3. Now, we want to prove that "m<1 + m<4 = m<3 + m<4".
To prove this, we can use the property of equality called Substitution. According to this property, if two quantities are equal, then you can replace one with the other without changing the truth of an equation.
In our given statement, we see that "m<2 = m<4", so we can substitute "m<2" with "m<4" in the equation "m<1 + m<2 = m<3 + m<4".
By doing this substitution, we get:
m<1 + m<4 = m<3 + m<4
Therefore, based on the Substitution property, the statement is justified. Hence, the correct answer is D. Substitution.