Question

Given: LM || SN and ∠LO = ∠MN

Prove: LMNO is a parallelogram.
A) Statements and reasons are needed for proof.
B) Definition of parallel lines
C) Substitution
D) Angle congruence

Answer 1

To prove that LMNO is a parallelogram, use the given information that LM || SN and ∠LO = ∠MN. Apply the properties of parallel lines and angle congruence to show that the opposite sides of the quadrilateral are parallel.

Step-by-step explanation:

To prove that LMNO is a parallelogram, we will use the given information that LM || SN and ∠LO = ∠MN. Our proof will involve the use of angle congruence and the definition of parallel lines.

1. LM || SN (Given)
2. ∠LO = ∠MN (Given)
3. LO || MN (Parallel lines have equal corresponding angles)
4. LM || NO (Transitive property of parallel lines)
5. LMNO is a parallelogram (Opposite sides of a parallelogram are parallel)