Question

Given: Line A B intersects Line D E at point C. Prove: AngleDCB Is-congruent-toAngleECA Line D E intersects line B A at point C. A 2-column table with 6 rows. Column 1 is labeled statements with the entries line A B intersects line D E at point C, angle D C B and angle B C E are a linear pair, angle D C B is supplementary to angle B C E, angle B C E and angle E C A are a linear pair, angle B C E is supplementary to angle E C A, angle D C B is-congruent-to angle E C A. Column 2 is labeled reasons with the entries given, definition of linear pair, linear pair post, definition of linear pair, question mark, congruent to supplementary theorem. What is the missing reason in step 5? linear pair postulate given definition of complementary angles congruent complements theorem

Answer 1

Answer:

The missing reason in step 5 is;

The linear pair postulate

Step-by-step explanation:

The information given are;

Column 1,                                                 Column 2

Statements,                                             Reasons

Line AB intersect DE at C,                      Given

∠DCB and ∠BCE are linear pair,           Definition of linear pair

∠DCB is supplementary to ∠BCE,         Linear pair postulate

∠BCE and ∠ECA are linear pair,           Definition of linear pair

∠BCE is supplementary to ∠ECA,         Linear pair postulate

∠DCB ≅ ∠ECA,                                      Congruent to supplementary theorem  

Therefore, the missing reason in step 5 is the linear pair postulate.