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: Analyze each option

• Linear pair postulate: States that if two angles form a linear pair, then they are supplementary. In step 3, it was used for \(\angle DCB\) and \(\angle BCE\).
• Given: Used for the initial information (step 1).
• Definition of complementary angles: Complementary angles sum to \(90^{\circ}\), but we are dealing with supplementary angles (\(180^{\circ}\)) here.
• Congruent complements theorem: Not relevant here.

Since \(\angle BCE\) and \(\angle ECA\) form a linear pair (from step 4, by the definition of a linear pair), by the linear - pair postulate (which says that if two angles form a linear pair, they are supplementary), \(\angle BCE\) is supplementary to \(\angle ECA\).

Answer:

linear pair postulate