Question

given the parallelogram below, michael writes, \segment \\(ac\\) is congruent to segment \\(ac\\).\ which of the following reasons allows him to write this statement?

a. reflexive property
b. corresponding parts of congruent polygons theorem
c. distributive property
d. symmetric property

Explanation:

Identify the geometric statement

$$ \overline{AC} \cong \overline{AC} $$

Apply the definition of geometric properties

$$ \text{Reflexive Property: } x = x \text{ or } \overline{XY} \cong \overline{XY} $$

$$ \text{Symmetric Property: If } a = b, \text{ then } b = a $$

$$ \text{Distributive Property: } a(b + c) = ab + ac $$

Match the statement to the correct property

$$ \overline{AC} \cong \overline{AC} \implies \text{Reflexive property} $$

Answer:

• A. Reflexive property (Correct answer)
• B. Corresponding parts of congruent polygons theorem
• C. Distributive property
• D. Symmetric property