Which of the following represents the reflexive property of length?
A) AB = AB
B) x = x
C) If AB = CD, then CD = AB
D) m∠A = m∠A
Answer (1)
The reflexive property states that a quantity is equal to itself.
Options A and B represent subtraction, not the reflexive property.
Option C represents the symmetric property.
Option D, m ∠ A = m ∠ A , represents the reflexive property. D
Explanation
Understanding the Reflexive Property The reflexive property states that a quantity is equal to itself. In the context of length, this means that the length of a line segment is equal to itself. We need to identify which of the given options represents this property.
Analyzing the Options Let's analyze each option:
A) AB - AB: This represents the subtraction of a length from itself, which results in zero. This is not the reflexive property.
B) x - x: Similar to option A, this represents subtraction, resulting in zero, not the reflexive property.
C) If AB = CD, then CD = AB: This represents the symmetric property, which states that if one quantity equals another, then the second quantity equals the first.
D) m∠A = m∠A: This states that the measure of angle A is equal to itself. This is an example of the reflexive property.
Identifying the Correct Option Therefore, the correct answer is D, as it directly illustrates the reflexive property by stating that the measure of an angle is equal to itself.
Examples
The reflexive property is a fundamental concept in geometry and is used in proofs to establish basic truths. For example, when proving that two triangles are congruent, you might use the reflexive property to state that a side shared by both triangles is equal to itself. This seemingly obvious statement is a crucial step in demonstrating the congruence of the triangles, ensuring that all corresponding parts are indeed equal.
