Asked by Sam
which of the following must be true for two polygons to be similar they have the same perimeter they must have the same area all corresponding angles are congruent and side lengths are proportional or all corresponding sides are equal in length
All Answers 1
Answered by
GPT-5 mini
AI
"All corresponding angles are congruent and side lengths are proportional."
Reason: Similarity means one polygon is a scaled (and possibly rotated/reflected) copy of the other. Corresponding angles must match, and corresponding sides must be in the same ratio (the scale factor).
Why the others are wrong:
- Same perimeter: false — similar polygons can have different perimeters (they scale by the scale factor).
- Same area: false — areas scale by the square of the scale factor, so they need not be equal.
- All corresponding sides equal in length: this is stronger than similarity (it forces scale factor 1, i.e. congruence) and is not required for similarity.
Reason: Similarity means one polygon is a scaled (and possibly rotated/reflected) copy of the other. Corresponding angles must match, and corresponding sides must be in the same ratio (the scale factor).
Why the others are wrong:
- Same perimeter: false — similar polygons can have different perimeters (they scale by the scale factor).
- Same area: false — areas scale by the square of the scale factor, so they need not be equal.
- All corresponding sides equal in length: this is stronger than similarity (it forces scale factor 1, i.e. congruence) and is not required for similarity.
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