Your friend tells you that reflecting a figure will make the figure’s angles smaller, so it is no longer congruent to the original figure. Is this true? Why or why not? In 3–5 sentences, explain your answer and describe an example that would verify your claim.
No, reflecting a figure does not change the measure of its angles. Reflection is a transformation that produces a mirror image of the original figure while maintaining the same distances and angles. The angles of a figure are determined by the relationships between its sides, and reflecting the figure does not alter the size of its sides or the relationships between them. For example, consider a triangle with angles measuring 60 degrees, 70 degrees, and 50 degrees. Reflecting this triangle would create a mirror image with the same angles measuring 60 degrees, 70 degrees, and 50 degrees.
In 3–5 sentences, describe the process you could use to determine if a shape is a reflection of a preimage. What features should stay the same and what should change from the preimage to the image? Give an example.
To determine if a shape is a reflection of a preimage, you need to compare the corresponding features of both the preimage and the image. The features that should stay the same are the distances between points and the angles between lines. The features that should change are the orientation or direction of the shape. For example, if you have a triangle and its reflection, you can compare the lengths of the sides and the angles between the lines to ensure they remain the same, while the position or direction of the triangle changes.
