Naming Quadrilaterals in a Coordinate Plane Worksheet - Students draw and identify quadrilaterals using given vertices.

Problem Overview:

The task involves identifying and naming quadrilaterals based on the vertices provided in a coordinate plane. The goal is to determine the type of quadrilateral formed by connecting the given points.

Solution Approach:

1. Identify the Coordinates: Extract the coordinates of the vertices from the graphs.
2. Connect the Points: Visualize or draw the quadrilateral by connecting the points in order.
3. Analyze the Shape: Use geometric properties to classify the quadrilateral:
- Parallelogram: Opposite sides are parallel and equal.
- Rectangle: Opposite sides are equal, and all angles are 90°.
- Rhombus: All sides are equal.
- Square: All sides are equal, and all angles are 90°.
- Trapezoid: One pair of opposite sides is parallel.
- Kite: Two pairs of adjacent sides are equal.
- Irregular Quadrilateral: Does not fit any of the above categories.

Detailed Analysis for Each Quadrilateral:

#### Quadrilateral 1:
- Vertices: \( X(2, 4) \), \( W(4, 2) \), \( Y(7, 4) \), \( Z(5, 6) \)
- Shape Analysis:
- Connect the points in order: \( X \to W \to Y \to Z \to X \).
- Observe that opposite sides appear to be parallel and equal in length.
- Check for right angles: The shape does not appear to have all 90° angles.
- Conclusion: This is a parallelogram.

#### Quadrilateral 2:
- Vertices: \( P(-2, 3) \), \( Q(2, 5) \), \( R(4, 3) \), \( S(0, -3) \)
- Shape Analysis:
- Connect the points in order: \( P \to Q \to R \to S \to P \).
- Observe that one pair of opposite sides (\( PQ \) and \( RS \)) appears to be parallel.
- The other pair of sides (\( PR \) and \( QS \)) are not parallel.
- Conclusion: This is a trapezoid.

#### Quadrilateral 3:
- Vertices: \( L(-2, 3) \), \( M(4, 3) \), \( N(5, -2) \), \( Q(-1, -2) \)
- Shape Analysis:
- Connect the points in order: \( L \to M \to N \to Q \to L \).
- Observe that opposite sides are parallel and equal in length.
- All angles appear to be 90°.
- Conclusion: This is a rectangle.

#### Quadrilateral 4:
- Vertices: \( S(-2, 6) \), \( V(0, -2) \), \( U(4, -2) \), \( T(2, 6) \)
- Shape Analysis:
- Connect the points in order: \( S \to V \to U \to T \to S \).
- Observe that opposite sides are parallel and equal in length.
- All sides appear to be equal in length.
- All angles appear to be 90°.
- Conclusion: This is a square.

Final Answers:

1. Quadrilateral 1: Parallelogram
2. Quadrilateral 2: Trapezoid
3. Quadrilateral 3: Rectangle
4. Quadrilateral 4: Square

Boxed Final Answer:

\[
\boxed{\text{Parallelogram, Trapezoid, Rectangle, Square}}
\]