Answer:
(A) Linear pair postulate
Step-by-step 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.
