Which statement represents the transitive property of equality?
A) If WX=XY, then XY= WX.
B) If WX=XY and XY=YZ, then WX=YZ.
C) If m∠A=m∠B, then m∠B=m∠A.
D) If x=y, then y = x.
Answer (2)
The transitive property of equality states that if a = b and b = c , then a = c . Among the given options, only option B, which states 'If WX = XY and XY = YZ, then WX = YZ,' correctly represents the transitive property.
The transitive property states: If a = b and b = c , then a = c .
Option A represents the symmetric property.
Option C represents the symmetric property.
Option D represents the symmetric property.
Option B correctly represents the transitive property: I f WX = XY and XY = YZ , then WX = YZ .
Explanation
Understanding the Transitive Property The question asks us to identify the statement that correctly demonstrates the transitive property of equality. The transitive property states that if two quantities are equal to the same quantity, then they are equal to each other. In mathematical terms, if a = b and b = c , then a = c . We will examine each option to determine which one fits this definition.
Analyzing the Options Let's analyze each option:
Option A: If WX = XY, then XY = WX. This statement represents the symmetric property of equality, which states that if a = b , then b = a .
Option B: If WX = XY and XY = YZ, then WX = YZ. This statement perfectly matches the definition of the transitive property of equality. If WX equals XY, and XY equals YZ, then WX must equal YZ.
Option C: If m∠A = m∠B, then m∠B = m∠A. This statement, like Option A, represents the symmetric property of equality.
Option D: If x = y, then y = x. This statement also represents the symmetric property of equality.
Identifying the Correct Statement Based on our analysis, Option B is the only statement that accurately represents the transitive property of equality.
Conclusion Therefore, the statement that represents the transitive property of equality is: If WX = XY and XY = YZ, then WX = YZ.
Examples
The transitive property is a fundamental concept in mathematics and is used in various real-life situations. For example, if you know that John is the same age as Mary, and Mary is the same age as Peter, then you can conclude that John is the same age as Peter. This kind of reasoning helps in making logical deductions and comparisons in everyday scenarios.
The transitive property of equality states that if one quantity equals a second, and that second equals a third, then the first quantity equals the third. Among the given options, only Option B accurately reflects this property. Therefore, the correct answer is: If WX = XY and XY = YZ, then WX = YZ.
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