Transformations, congruence, and proof

📐

6 subtopics

120 questions

Precise definitions of geometric terms (point, line, plane, angle, circle) Translations, reflections, rotations Symmetry (reflectional and rotational) Compositions of transformations Congruence in terms of rigid motions +1 more

Lines and angles

📐

3 subtopics

60 questions

Angle theorems (vertical, complementary, supplementary) Parallel lines cut by a transversal (alternate interior, corresponding, co-interior) Perpendicular bisector theorem (equidistance)

Triangle theorems

📐

5 subtopics

100 questions

Triangle angle sum and exterior angle theorems Isosceles and equilateral triangle theorems Midsegment theorem Medians, altitudes, perpendicular bisectors, angle bisectors Triangle inequality and side/angle relationships

Quadrilateral theorems

📐

3 subtopics

60 questions

Parallelogram theorems (opposite sides, angles, diagonals) Properties of rectangle, square, rhombus, kite, trapezoid Proving a quadrilateral is a specific type

Proof and reasoning

📐

5 subtopics

100 questions

Inductive vs deductive reasoning; counterexamples Conditional statements (converse, inverse, contrapositive, biconditional) Proof formats (two-column, paragraph, flow chart) Proofs by induction and contradiction Spherical / non-Euclidean geometry comparison

Geometric constructions

📐

3 subtopics

60 questions

Basic constructions (segment, angle, bisectors, perpendiculars, parallels) Construct equilateral triangle, square, regular hexagon inscribed in circle Triangle Inequality theorem via construction

Similarity

📐

6 subtopics

80 questions

Similarity transformations and dilations Triangle similarity (AA, SAS, SSS) Triangle Proportionality theorem Scale drawings Geometric mean (altitude to hypotenuse of a right triangle) +1 more

Right triangles and trigonometry

📐

8 subtopics

160 questions

Pythagorean theorem (proof from similarity) Trigonometric ratios (sin, cos, tan) for acute angles Sine and cosine of complementary angles Solving right triangles (mixed contexts) Special right triangles (30-60-90, 45-45-90) and Pythagorean triples +3 more

Circles

📐

10 subtopics

200 questions

All circles are similar Central angles, inscribed angles, and arcs Chords and arcs (theorems and relationships) Tangent lines (radius perpendicular at point of tangency) Tangent from an external point (construction) +5 more

Two-dimensional measurement

📐

4 subtopics

80 questions

Area of polygons (triangles, quadrilaterals) Area of regular polygons (using apothem) Composite 2D figures (combining shapes for area) Perimeter and area on the coordinate plane

Three-dimensional measurement

📐

7 subtopics

140 questions

Surface area (prisms, pyramids, cones, cylinders, spheres) Lateral vs total surface area Volume (prisms, pyramids, cones, spheres, cylinders) Composite 3D figures (surface area and volume) Informal volume arguments (Cavalieri's principle, dissection) +2 more

Coordinate geometry

📐

5 subtopics

100 questions

Distance and midpoint formulas Partition of a directed line segment in a given ratio Slope criteria for parallel and perpendicular lines Equations of parallel and perpendicular lines Proving geometric theorems using coordinates

Modelling with geometry

📐

3 subtopics

60 questions

Modelling real-world objects with geometric shapes Density (area-based and volume-based) Design problems with geometric constraints

Probability and statistics

📐

8 subtopics

160 questions

Sample spaces, events, unions, intersections, complements Independent events and the Multiplication Rule Conditional probability Two-way frequency tables Addition Rule for probability +3 more

USA - Geometry