Is your new house after this transformation congruent to the original house? Explain

your answer

No, the new house is not congruent to the original house. Congruent shapes are identical in size and shape, meaning that all sides and angles are equal. After a transformation, the size and shape of the house may have changed, making it no longer congruent to the original house.

To determine if the new house after the transformation is congruent to the original house, we need to compare their corresponding parts and check if they have the same shape and size. Here's how you can go about it:

1. Identify the transformation: Determine what type of transformation has been applied to the original house. Common types of transformations include translations, rotations, reflections, and dilations.

2. Compare corresponding parts: Take a close look at different parts of the original and transformed houses that correspond to each other. For example, compare the positions and orientations of walls, windows, doors, and other structural features.

3. Check for congruence criteria: Depending on the type of transformation, different criteria will indicate congruence. Here are some common congruence criteria:

- Translations: If the transformation is a pure translation (moving the entire house without changing its shape or size), then the new house will be congruent to the original house.

- Rotations: If the transformation is a rotation (turning the original house around a fixed point), the new house will be congruent if the angle of rotation and the center of rotation are the same.

- Reflections: If the transformation is a reflection (flipping the original house over a mirror line), the new house will be congruent if the mirror line and orientation are the same.

- Dilations: If the transformation is a dilation (changing the size of the original house while maintaining its shape), the new house will be congruent if the scale factor and center of dilation are the same.

4. Assess congruence: Compare the corresponding parts of the original and transformed houses based on the congruence criteria mentioned above. If the corresponding parts satisfy the criteria, then the new house is congruent to the original house.

Remember, determining congruence relies on careful observation and comparison between the original and transformed houses.

To determine if the new house after the transformation is congruent to the original house, we need to consider a few key factors.

1. Size: Are the dimensions of the new house the same as the original house? If the lengths, heights, and widths of both houses are identical, this suggests that they are congruent.

2. Shape: Do the new and original houses have the same shape? If the overall shape of the houses remains unchanged, it suggests congruence. However, if the shapes are different, it is unlikely that they are congruent.

3. Angles: Are the angles within the new house the same as those in the original house? If the angles are congruent, it indicates that the houses are likely congruent. However, if there are variations in the angles, it suggests non-congruence.

4. Symmetry: Does the new house possess the same symmetry properties as the original house? If both houses have the same line or point of symmetry, it suggests congruence. Conversely, if the symmetry properties differ, the houses may not be congruent.

By considering these factors, we can evaluate whether the new house after the transformation is congruent to the original house.