Geometry & Measurement

Proofs & Deductive Reasoning

Key congruence postulates: SSS, SAS, ASA, AAS, HL (right triangles).

Common proof strategies: use given information + definitions + postulates to derive the required conclusion step by step.

Advanced Circles

• Power of a point: PA × PB = PC × PD (intersecting chords); PA × PB = PC² (secant-tangent)
• Inscribed angle theorem: inscribed angle = ½ central angle on same arc
• Tangent-tangent angle: = ½|difference of intercepted arcs|

3D Geometry

• Cross-sections of solids: a sphere cut by a plane → circle; a cone cut parallel to base → circle; obliquely → ellipse
• Similar solids with ratio k: volumes are in ratio k³; surface areas in ratio k²
• Cavalieri's principle: if two solids have equal cross-section areas at every height, they have equal volumes