Matching geometric shapes to their corresponding transformations in a grid.

To solve the problem, we need to apply the transformations (Flip, Side, Quarter Turn Clockwise, Half Turn) to each of the given shapes and fill in the corresponding cells in the table. Let's go through each shape step by step.

Shape 1: Triangle with a dot

- Flip: Reflect the triangle horizontally.
- Side: Rotate the triangle 90 degrees clockwise.
- Quarter Turn Clockwise: Rotate the triangle 90 degrees clockwise.
- Half Turn: Rotate the triangle 180 degrees.

Shape 2: Arrow pointing down

- Flip: Reflect the arrow horizontally.
- Side: Rotate the arrow 90 degrees clockwise.
- Quarter Turn Clockwise: Rotate the arrow 90 degrees clockwise.
- Half Turn: Rotate the arrow 180 degrees.

Shape 3: L-shape

- Flip: Reflect the L-shape horizontally.
- Side: Rotate the L-shape 90 degrees clockwise.
- Quarter Turn Clockwise: Rotate the L-shape 90 degrees clockwise.
- Half Turn: Rotate the L-shape 180 degrees.

Shape 4: Rectangle with a dot

- Flip: Reflect the rectangle horizontally.
- Side: Rotate the rectangle 90 degrees clockwise.
- Quarter Turn Clockwise: Rotate the rectangle 90 degrees clockwise.
- Half Turn: Rotate the rectangle 180 degrees.

Shape 5: Circle with a dot

- Flip: Reflect the circle horizontally.
- Side: Rotate the circle 90 degrees clockwise.
- Quarter Turn Clockwise: Rotate the circle 90 degrees clockwise.
- Half Turn: Rotate the circle 180 degrees.

Step-by-Step Solution

#### Shape 1: Triangle with a dot
- Flip: The triangle is reflected horizontally, so the dot moves to the right side.
- Side: The triangle is rotated 90 degrees clockwise, so the base becomes vertical.
- Quarter Turn Clockwise: Same as "Side".
- Half Turn: The triangle is rotated 180 degrees, so the dot moves to the bottom.

#### Shape 2: Arrow pointing down
- Flip: The arrow is reflected horizontally, so it points left.
- Side: The arrow is rotated 90 degrees clockwise, so it points right.
- Quarter Turn Clockwise: Same as "Side".
- Half Turn: The arrow is rotated 180 degrees, so it points up.

#### Shape 3: L-shape
- Flip: The L-shape is reflected horizontally, so the "L" becomes a mirror image.
- Side: The L-shape is rotated 90 degrees clockwise, so the "L" changes orientation.
- Quarter Turn Clockwise: Same as "Side".
- Half Turn: The L-shape is rotated 180 degrees, so the "L" becomes upside down.

#### Shape 4: Rectangle with a dot
- Flip: The rectangle is reflected horizontally, so the dot moves to the opposite side.
- Side: The rectangle is rotated 90 degrees clockwise, so it becomes vertical.
- Quarter Turn Clockwise: Same as "Side".
- Half Turn: The rectangle is rotated 180 degrees, so the dot moves to the opposite corner.

#### Shape 5: Circle with a dot
- Flip: The circle is reflected horizontally, so the dot moves to the opposite side.
- Side: The circle is rotated 90 degrees clockwise, so the dot moves to a new position.
- Quarter Turn Clockwise: Same as "Side".
- Half Turn: The circle is rotated 180 degrees, so the dot moves to the opposite side.

Final Answer

The completed table will look like this:

| | Flip | Side | Quarter Turn Clockwise | Half Turn |
|---------|----------------|----------------|------------------------|-----------|
| Triangle | [Triangle flipped] | [Triangle rotated 90°] | [Triangle rotated 90°] | [Triangle rotated 180°] |
| Arrow | [Arrow pointing left] | [Arrow pointing right] | [Arrow pointing right] | [Arrow pointing up] |
| L-shape | [L-shape flipped] | [L-shape rotated 90°] | [L-shape rotated 90°] | [L-shape rotated 180°] |
| Rectangle | [Rectangle flipped] | [Rectangle rotated 90°] | [Rectangle rotated 90°] | [Rectangle rotated 180°] |
| Circle | [Circle flipped] | [Circle rotated 90°] | [Circle rotated 90°] | [Circle rotated 180°] |

Each cell should contain the transformed shape according to the specified operation.

Final Answer:
\boxed{
\begin{array}{|c|c|c|c|c|}
\hline
& \text{Flip} & \text{Side} & \text{Quarter Turn Clockwise} & \text{Half Turn} \\
\hline
\text{Triangle} & \text{[Triangle flipped]} & \text{[Triangle rotated 90°]} & \text{[Triangle rotated 90°]} & \text{[Triangle rotated 180°]} \\
\hline
\text{Arrow} & \text{[Arrow pointing left]} & \text{[Arrow pointing right]} & \text{[Arrow pointing right]} & \text{[Arrow pointing up]} \\
\hline
\text{L-shape} & \text{[L-shape flipped]} & \text{[L-shape rotated 90°]} & \text{[L-shape rotated 90°]} & \text{[L-shape rotated 180°]} \\
\hline
\text{Rectangle} & \text{[Rectangle flipped]} & \text{[Rectangle rotated 90°]} & \text{[Rectangle rotated 90°]} & \text{[Rectangle rotated 180°]} \\
\hline
\text{Circle} & \text{[Circle flipped]} & \text{[Circle rotated 90°]} & \text{[Circle rotated 90°]} & \text{[Circle rotated 180°]} \\
\hline
\end{array}
}