Question

given: (overleftrightarrow{ab}) intersects (overleftrightarrow{de}) at point c. prove: (angle dcbcongangle eca) what is the missing reason in step 5? linear pair postulate given definition of complementary angles congruent complements theorem statements reasons 1 (overleftrightarrow{ab}) intersects (overleftrightarrow{de}) at point c 1 given 2 (angle dcb) and (angle bce) are a linear pair 2 def. of ln pr 3 (angle dcb) is supp to (angle bce) 3 linear pair post 4 (angle bce) and (angle eca) are a linear pair 4 def of ln pr 5 (angle bce) is supp to (angle eca) 5? 6 (angle dcbcongangle eca) 6 (cong) supp. thm

Explanation:

A linear - pair of angles are adjacent and supplementary. Since ∠BCE and ∠ECA are a linear pair (by the definition of a linear pair), according to the linear - pair postulate, they are supplementary.

Answer:

linear pair postulate