Label the elements of plot

Answer 1

The elements of plot are the essential components that structure a narrative. Here are the primary elements:

1. Exposition: This is the introduction of the story where the setting, characters, and basic situation are established.

2. Rising Action: This phase involves the events that lead to the conflict. Tensions build as challenges and obstacles arise for the characters.

3. Climax: The climax is the turning point of the story, where the main conflict reaches its peak. This moment often leads to a change for the protagonist.

4. Falling Action: In this part, the consequences of the climax unfold. The tension decreases as the story moves towards resolution.

5. Resolution (or Denouement): This is the conclusion of the story where conflicts are resolved and the story comes to a close, providing closure for the characters and the audience.

These elements work together to create a cohesive and engaging narrative structure.

Answer 2

Given: JN ≅ NL; <JMK ≅ <LKM
Prove: JKLM is a parallelogram

Answer 3

To prove that the quadrilateral \( JKLM \) is a parallelogram given that \( JN \cong NL \) and \( \angle JMK \cong \angle LKM \), we can use one of the properties of parallelograms related to sides and angles. Here’s a structured proof:

Given:

1. \( JN \cong NL \) (the segments \( JN \) and \( NL \) are congruent).
2. \( \angle JMK \cong \angle LKM \) (the angles \( JMK \) and \( LKM \) are congruent).

To Prove:

\( JKLM \) is a parallelogram.

Proof:

1. Consider the segments: Since \( JN \cong NL \), we know that segment \( JL \) (formed by adding segments \( JN \) and \( NL \)) is parallel to segment \( KM \). This is a direct consequence of the definition of a parallelogram, where opposite sides are equal in length.

2. Consider the angles: Since \( \angle JMK \cong \angle LKM \), this implies that the angles between the sides are equal.

3. Apply the properties of parallel lines: Since we have established that the lengths of opposite sides are congruent and the angles formed by the lines with respect to a transversal (here, we can consider line \( JM \) and line \( KL \) with transversal \( JK \)) are equal, we can use the converse of the Alternate Interior Angles Theorem, which states that if a transversal intersects two lines such that the alternate interior angles are congruent, then the two lines are parallel.

4. Conclude with properties of parallelograms: Since we've established both pairs of opposite sides \( JN \) and \( NL \) are congruent, as well as the equality of corresponding angles \( \angle JMK \cong \angle LKM \), we conclude by using the properties of parallelograms: if one pair of opposite sides of a quadrilateral are both equal and parallel, then the quadrilateral is a parallelogram.

Therefore, \( JKLM \) is a parallelogram.

Conclusion:

Hence, we have proved that quadrilateral \( JKLM \) is a parallelogram based on the given information.