Determine whether the statement is true or false. Explain or show your reasoning.

1. The shape is a rectangle.
2. The shape is a square.
3. The shape is a rhombus.

1. Draw a trapezoid that is also a parallelogram. Explain how you know it is a trapezoid and a parallelogram.

   

2. Draw a trapezoid that is not a parallelogram. Explain how you know it is a trapezoid but not a parallelogram.

   

Determine if it’s possible to draw each shape so it contains the 2 sides drawn on the grid. Explain your reasoning.

1. a square
2. a rectangle
3. a rhombus

Decide if each statement is true or false. Explain or show your reasoning.

1. A parallelogram is sometimes a rhombus.
2. A rhombus is always a parallelogram.
3. A trapezoid is never a rectangle.
4. A rectangle is never a square.
5. A parallelogram is always a trapezoid.

Draw a right triangle on the grid to match each description. If you think there is no such triangle, explain why.

1. It has 2 equal side lengths.

   

2. It has 3 equal side lengths.

   

3. It has 3 different side lengths.

   

1. Jada cut a quadrilateral in half, from 1 vertex to the opposite vertex, and she got 2 triangles that each have exactly 2 equal side lengths. What kind of quadrilateral could Jada have cut in half? Explain or show your reasoning.

2. Elena put together 2 right triangles to make a quadrilateral. What kind of quadrilateral could Elena have made? Explain or show your reasoning.

1. Can you draw a square on the grid that does not have a vertical or horizontal side? Explain or show your reasoning.

   

2. Draw the line segment from \((4, 4)\) to \((6, 5)\). Can you draw a square that contains this segment as one of its sides? Explain or show your reasoning.