In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.  

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.  

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.  

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar. 

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar. 

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar. 

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

• Rotation: A rotation means turning an image, shape, line, etc. around a central point.
• Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
• Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar. 

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and . 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are vertical angles; thus, both angle  and  are congruent and equal 

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and . 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are corresponding angles; thus, both angle  and  are congruent and equal 

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and . 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are corresponding angles; thus, both angle  and  are congruent and equal