Question

Use the image to answer question.

A parallelogram with vertices upper A upper B upper C upper D.

If ΔABC≅ΔCDA
, then AC¯¯¯¯¯¯¯¯
(the diagonal of the quadrilateral) ≅AC¯¯¯¯¯¯¯¯
by which of the following properties?

Option #1: Division Property of Equality

Option #2: Reflexive Property of Equality

Option #3: Transitive Property of Equality

Option #4: Substitution Property of Equality

(1 point)
AC¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯
by Option #
.

Answer 1

To determine which property justifies the statement \( AC \cong AC \), we need to analyze the options given.

1. **Division Property of Equality**: This property typically involves dividing both sides of an equation by the same value. It does not apply here.

2. **Reflexive Property of Equality**: This property states that any geometric figure is congruent to itself. Therefore, \( AC \cong AC \) is a direct application of the Reflexive Property.

3. **Transitive Property of Equality**: This property states that if \( a = b \) and \( b = c \), then \( a = c \). It does not apply here since we are not comparing three different segments.

4. **Substitution Property of Equality**: This property allows you to replace one quantity with another equivalent quantity. It's not applicable to the direct relationship of a line segment to itself.

Given this analysis, the correct property that applies here is:

**AC ≅ AC by Option #2: Reflexive Property of Equality.**