Relative positions of two lines
Intersecting (one common point), parallel (no common point, coplanar), or skew (non-coplanar).
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Lesson overview
This lesson brings together the PDF, study notes and chapter flow so you can revise Geometry in Space without losing the thread.
Relative positions of two lines
Intersecting (one common point), parallel (no common point, coplanar), or skew (non-coplanar).
Plane defined by 3 non-collinear points
Three non-collinear points A, B, C define a unique plane (ABC).
Three perpendiculars theorem
If D is ⊥ to plane P, and D' is ⊥ to D, then D' lies in plane P.
Cube with side a
Volume = a³. Total area = 6a². Diagonal = a√3.
Rectangular box
Volume = l·L·h. Diagonal = √(l²+L²+h²).
Pyramid
Volume = (1/3) · Base area · height.
Sphere of radius r
Volume = (4/3)πr³. Area = 4πr².
Problem-solving method
Identify data, set formulas, solve step by step, then verify sign, unit, and coherence.
Common mistakes
Forgetting domain constraints, mixing equality/equivalence, and losing solutions during transformations.