Plane Geometry
What this domain tests
Angle chasing with parallel lines, triangle congruence and similarity, and circle angle facts, normally fitted into a two- or three-step calculation.
Core rules
- Angles on a straight line sum to 180°, around a point to 360°. Interior angles of an n-gon sum to (n−2)×180°. An exterior angle of a triangle equals the sum of the two remote interior angles.
- With parallel lines: corresponding and alternate angles are equal, co-interior angles sum to 180°.
- Congruence conditions: SSS, SAS, ASA (the side must lie between the two angles), and RHS for right triangles. AAA gives similarity, not congruence.
- Similar triangles have equal angles and corresponding sides in a fixed ratio k; their areas are in ratio k².
- Circle facts: the angle at the centre is twice the inscribed angle on the same arc; angles in the same segment are equal; the angle in a semicircle is 90°; a tangent is perpendicular to the radius at the point of contact.
Worked example
A, B and C lie on a circle with centre O, and ∠AOB = 110°, with C on the major arc. Then ∠ACB = 110° ÷ 2 = 55°. Had C been on the minor arc, the inscribed angle would subtend the major arc and equal 180° − 55° = 125°.
Traps that cost marks
Using the reflex central angle; treating SSA as a congruence test; assuming a diagram is drawn to scale; applying a length ratio to an area.