Question

given \\( \overleftrightarrow{ab} \\) intersects \\( \overleftrightarrow{de} \\) at point c
prove \\( \angle dcb \cong \angle eca \\)
what is the missing reason in step 5?
linear pair postulate
given
definition of complementary angles
congruent complements theorem

Explanation:

Step1: Recall linear pair postulate

The linear pair postulate states that if two angles form a linear pair, then they are supplementary. In this proof, since \(\angle DCB\) and \(\angle DCE\) form a linear pair (statement 2), by the linear pair postulate (reason 3) \(\angle DCB\) is supplementary to \(\angle DCE\). Similarly, for \(\angle DCE\) and \(\angle ECA\) (statements 4 and 5), the reason for \(\angle DCE\) being supplementary to \(\angle ECA\) (step 5) is the linear pair postulate.

Answer:

linear pair postulate