Geometry
Proofs, transformations, circles and solid geometry
Explanation
Transformations
- Translation: slide — every point moves the same distance in the same direction.
- Reflection: flip over a line (axis of reflection).
- Rotation: turn around a point by a given angle.
- Dilation: scale up or down from a centre point by a scale factor.
Circles
- Circumference: C = 2πr = πd
- Area: A = πr²
- Arc length: (central angle/360°) × 2πr
- Sector area: (central angle/360°) × πr²
Solid Geometry
| Solid | Volume | Surface Area |
|---|---|---|
| Rectangular prism | lwh | 2(lw+lh+wh) |
| Cylinder | πr²h | 2πr² + 2πrh |
| Cone | ⅓πr²h | πr² + πrl (l=slant height) |
| Sphere | ⁴⁄₃πr³ | 4πr² |
Practice Questions
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What does Geometry cover in the ISEE Middle Level exam?
Proofs, transformations, circles and solid geometry.
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