Question

given quadrilateral mnol with mn ≅ lo and ml ≅ no. prove mnol is a parallelogram. complete the paragraph proof. we are given that mn ≅ lo and ml ≅ no. we can draw in mo because between any two points is a line. by the reflexive property, mo ≅ mo. by sss, △mlo ≅ △blank. by cpctc, ∠lmo ≅ ∠blank and ∠nmo ≅ ∠lom. both pairs of angles are also blank based on the definition. based on the converse of the alternate interior angles theorem, mn ∥ lo and lm ∥ no. based on the definition of a parallelogram, mnol is a parallelogram.

Explanation:

Step1: Identify congruent triangles

Since $MN\cong LO$, $ML\cong NO$ and $MO\cong MO$ (reflexive property), by SSS (Side - Side - Side) congruence criterion, $\triangle MLO\cong\triangle NOM$.

Step2: Use CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent). So, $\angle LMO\cong\angle NOM$ and $\angle NMO\cong\angle LOM$.

Step3: Determine parallel sides

These pairs of angles are alternate interior angles. By the converse of the alternate - interior angles theorem, if alternate interior angles are congruent, then the lines are parallel. So, $MN\parallel LO$ and $LM\parallel NO$.

Step4: Apply parallelogram definition

A parallelogram is defined as a quadrilateral with two pairs of parallel sides. Since $MN\parallel LO$ and $LM\parallel NO$, $MNOL$ is a parallelogram.

Answer:

The blanks should be filled as follows: $\triangle NOM$; $\angle NOM$; alternate interior angles.