Question

proof:

statement	reason
2. create point $d$ on $\overline{ac}$ so that $\overline{bd}$ bisects $\angle abc$ as shown.	constructing an angle bisector
3. $m\angle abd = m\angle dbc$	definition of angle bisector
4. $bd = bd$
5. $\triangle abd \cong \triangle cbd$	sas
6. $m\angle bac = m\angle bca$	corresponding angles of congruent triangles are equal.

47
what is the reason for statement 4 in this proof?
a. transitive property of equality
b. definition of midpoint
c. definition of parallel lines
d. reflexive property of equality

Explanation:

Statement 4 states $BD = BD$, which means a segment is equal to itself. This matches the Reflexive Property of Equality, which states that any quantity is equal to itself. The other options do not apply: the Transitive Property involves three quantities, the midpoint definition relates to segment division, and parallel lines involve angle/segment relationships between distinct lines.

Answer:

D. Reflexive Property of Equality