Similar figures have the same shape even when their sizes differ: corresponding angles are equal, and corresponding side lengths have a common scale factor, including enlargements, reductions, rotations, and reflections. The understanding distinguishes similarity from merely having the same area or one matching length and provides an informal foundation for proportional reasoning; formal similarity proofs, theorem-based criteria, and advanced geometric applications are not included.
Similar figures have the same shape, but they may be different sizes. One figure can be enlarged, reduced, rotated, or reflected to match the other.
To recognize similar figures:
Rectangle is cm wide and cm long. Rectangle is cm wide and cm long. Are they similar?
Step 1: Compare the angles.
Both rectangles have four right angles, so all corresponding angles are equal.
Step 2: Compare corresponding side lengths.
Match the widths and the lengths:
and
Both side lengths are multiplied by .
Step 3: Decide.
The angles match, and every corresponding side has the same scale factor. Therefore, the rectangles are similar.
Rectangle is an enlargement of rectangle by a scale factor of .
Remember: Figures are not similar just because they have the same area or one matching side. Their angles must match, and all corresponding sides must change by the same scale factor.
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