Question

Geometry Proof:

Given: LM > ON and LO ∠ MN
Prove: LMNO is a parallelogram.
Angles Segments Triangles Statements Reasons:

SSS
CPCTC
def. of parallelogram
converse of the alt. int. ∠s theorem
M

Answer 1

To prove that LMNO is a parallelogram, we can use the given information and the properties of parallelograms. First, we know that LM is greater than ON. This suggests that LMNO might be a trapezoid. However, since LO and MN are alternate interior angles, we can use the converse of the alternate interior angles theorem to conclude that LMNO is a parallelogram.

Step-by-step explanation:

To prove that LMNO is a parallelogram, we can use the given information and the properties of parallelograms. First, we know that LM is greater than ON.

This suggests that LMNO might be a trapezoid. However, since LO and MN are alternate interior angles, we can use the converse of the alternate interior angles theorem to conclude that LMNO is a parallelogram.

We can also use the Side-Side-Side (SSS) congruence criterion and the Converse of the Corresponding Parts of Congruent Triangles (CPCTC) to prove that LMNO is a parallelogram.

By showing that the corresponding sides LM and ON are congruent and that the corresponding angles LMN and ONO are congruent, we can establish the congruence of the two triangles LMO and NOL. Therefore, LMNO is a parallelogram.