Question

what does similarity require?
same perimeter
same shape and area
equal angles and equal side lengths
equal angles and proportional side lengths
question 3
a rectangle is dilated with a scale factor of 3/5. which of the following is true about the image?
the image is flipped
the image is not proportional
the image is similar to the original rectangle

Explanation:

For question 2:

• Similarity in geometry means that two figures have the same shape. This is defined by having equal corresponding angles and proportional corresponding side lengths.
• Same perimeter is not a requirement for similarity. For example, two similar triangles can have different perimeters.
• Same shape and area would imply congruence (which is a special case of similarity with a scale factor of 1), but similarity allows for different sizes (so different perimeters and areas).
• Equal angles and equal side lengths is the definition of congruence, not just similarity.

For question 3:

• Dilation is a transformation that changes the size of a figure but not its shape.
• When a rectangle is dilated with a scale factor of \(\frac{3}{5}\), the angles of the rectangle remain \(90^{\circ}\) (so angles are equal) and the side lengths are in proportion (the ratio of corresponding side lengths of the image and the original is \(\frac{3}{5}\)).
• Flipping is a reflection transformation, and dilation is not a reflection.
• Since dilation preserves the shape (by keeping angles equal and side - lengths proportional), the image is similar to the original rectangle.

Answer:

Question 2: Equal angles and proportional side lengths
Question 3: The image is similar to the original rectangle