Unlocking the Secrets of Similar Polygons: Shape, Size, and Proportions!
Similar polygons have equal corresponding angles and proportional corresponding sides. The ratio of their perimeters equals the scale factor, while the ratio of their areas equals the scale factor squared.
- Angles: Every corresponding angle in one polygon must be congruent to its counterpart in the other polygon.
- Sides: The lengths of corresponding sides of the polygons must be in the same ratio.
Worked examples: similar polygons
Practice questions on similar polygons
- Quadrilaterals (MNPQ) and (RSTU) have sides measuring (2 text{ cm}), (3 text{ cm}), (4 text{ cm}), (6 text{ cm}) and (4 text{ cm}), (6 text{ cm}), (8 text{ cm}), (12 text{ cm}) respectively. Are they similar?
- Two triangles (GHI) and (JKL) have angles measuring (45^circ), (45^circ), and (90^circ) for both. If (GH = 7 text{ cm}), (HI = 10 text{ cm}) and (JK = 14 text{ cm}), (KL = 20 text{ cm}), are they similar?
- Yes, they are similar.
- Yes, they are similar.
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