Subject
Geometry
Lines, angles, triangles, polygons, circles, and solids — plus the proofs and trig that hold them together.
Begin at I if you’re new to Geometry.
Points, Lines, and Angles
The vocabulary that everything else builds on. Classify angles and count parts of basic objects.
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Angle Pairs
Complementary, supplementary, vertical, and linear-pair relationships. Once you spot them, the algebra is one subtraction.
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Parallel Lines and Transversals
Eight angles, two distinct measures. Spot the pair type and you're one step from the answer.
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Triangle Angle Sum
The three interior angles of any triangle sum to 180°. Pair that with isosceles and exterior-angle facts.
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Triangle Congruence
Five shortcuts that prove two triangles are congruent: SSS, SAS, ASA, AAS, and HL for right triangles.
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Triangle Similarity
Similar triangles have proportional sides and equal angles. Use AA, SAS, or SSS similarity, then cross-multiply.
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Special Right Triangles
45-45-90 has ratio 1:1:√2. 30-60-90 has ratio 1:√3:2. Memorize them; skip the Pythagorean theorem.
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Right Triangle Trigonometry
SOH-CAH-TOA: three ratios that turn right triangles into angle problems and back.
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Polygon Angles
Interior sum = (n-2)·180°. Exterior sum = 360°, always. Regular polygons divide evenly.
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Quadrilateral Properties
Parallelogram, rectangle, rhombus, square, trapezoid, kite — each has its own angle, side, and diagonal rules.
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Circle Basics
Radius, diameter, chord, arc, central angle. Central angle equals the arc it intercepts.
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Inscribed Angles and Circle Theorems
Inscribed angle = half its intercepted arc. Semicircle inscribed = 90°. Cyclic quadrilateral opposite angles sum to 180°.
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Circumference and Arc Length
Circumference = 2πr. An arc is a fraction of that circumference set by the central angle.
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Circle Area and Sectors
Area = πr². A sector takes a fraction proportional to its central angle.
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Areas of Polygons
Each shape gets its own area formula. Memorize seven of them and you cover the curriculum.
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Surface Area
Total outer area of a 3D solid. One formula per shape — memorize them.
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Volume
Prisms/cylinders: base times height. Cones/pyramids: one-third of the matching prism. Sphere: (4/3)πr³.
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Transformations
Translations, reflections, rotations, and dilations. Each one is a coordinate-plane move with a tidy formula.
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