Plane Geometry
Core concepts
Master triangle congruence and similarity, the Pythagorean theorem, angle properties of parallel lines, circle theorems (inscribed angle, tangent–chord, power of a point), area and perimeter formulas, and coordinate geometry (distance, midpoint, slope).
Traps
- Similarity ratio vs area ratio: areas scale by the square of the linear ratio; volumes by the cube.
- Inscribed angle theorem: the central angle is twice the inscribed angle subtending the same arc.
- SSA is not a congruence criterion (ambiguous case).
- Angle sum confusion: exterior angle equals the sum of the two remote interior angles.
- Circle tangent: a tangent meets the radius perpendicularly.
Rule of thumb
When triangles share an angle or are formed by parallel lines, look for similarity; then set up a proportion.
Worked example
A triangle has sides 6, 8, 10. Is it right? Check 6² + 8² = 36 + 64 = 100 = 10². Yes, it is right-angled, with the right angle opposite the side of length 10. Its area is (1/2)(6)(8) = 24.