Question

What is the missing reason in step 5

A. Linear pair postulate

B. Givin

C. Definition of complementary angles

D. Congruent complements theorem

Answer 1

(A) Linear pair postulate

Explanation:

Given: AB intersects DE at point C.

To prove: ∠DCB≅∠ECA

Proof:

Statements Reasons

1. AB intersects DE at point C. given

2. ∠DCB and ∠BCE are a linear pair Definition of linear pair

3. ∠DCB is supplementary to ∠BCE Linear pair postulate

4. ∠BCE and ∠ECA are a linear pair Definition of linear pair

5. ∠BCE is supplementary to ∠ECA Linear pair postulate

Thus, from statement 2 and 5, we have

∠DCB+∠BCE=180° and ∠BCE+∠ECA=180°

⇒∠DCB+∠BCE=∠BCE+∠ECA

⇒∠DCB≅∠ECA

Hence proved

thus, option A is correct.