Similar, said precisely
Show on a big screenA photo is printed bigger. Every part grows. The shape stays the same.
Same shape
Shapes are similar when one is a scaled copy of the other. The copy may be bigger, smaller or equal. For polygons, matching parts sit in the same place. Then two things must hold. Matching angles are equal. Matching sides are in one ratio, the scale factor.
A polygon is a closed flat shape with straight sides.
Two polygons are similar when their matching angles are equal. Their matching sides are in one ratio.
Any two squares are similar. Any two equilateral triangles are similar. Any two circles are similar. Two rectangles need not be. Their side ratios can differ.
Check a pair
Triangle 3, 4, 5 and triangle 6, 8, 10. Match longest with longest.
| Small side | Large side | Ratio |
|---|---|---|
| 3 | 6 | 2 |
| 4 | 8 | 2 |
| 5 | 10 | 2 |
Every ratio is 2. The figure marks equal angles too. The triangles are similar, with scale factor 2.
A congruent pair has the same size and shape. It is similar too, with scale factor 1. But a similar pair need not be congruent.
Decide for seven pairs.
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Try the lab to finish this lesson.