Praxis Geometry cheat sheet
Praxis Geometry · Keep the key ideas within reach.
Geometry Content Knowledge
Angle relationships: vertical angles are equal; linear pairs sum to 180°; complementary angles sum to 90°; supplementary angles sum to 180°.
Parallel lines cut by a transversal: alternate interior angles are equal, corresponding angles are equal, and same-side interior angles are supplementary.
Triangle angle sum is 180°; an exterior angle equals the sum of the two remote interior angles; the largest angle faces the longest side.
Congruence criteria: SSS, SAS, ASA, AAS, and HL (right triangles only). SSA and AAA do not guarantee congruence; AAA gives similarity only.
Similarity criteria: AA, SSS~, and SAS~. Corresponding sides are proportional and corresponding angles are equal; the ratio of areas equals the square of the scale factor.
Pythagorean theorem: a² + b² = c² for right triangles; common triples are 3-4-5, 5-12-13, 8-15-17, and 7-24-25, plus their multiples.
Special right triangles: 45-45-90 has sides in ratio 1:1:√2; 30-60-90 has sides in ratio 1:√3:2, with the short leg opposite the 30° angle.
Circle facts: inscribed angle is half its intercepted arc; an angle formed by two chords equals half the sum of intercepted arcs; a tangent is perpendicular to the radius at the point of tangency.
Area and volume: circle A = πr², triangle A = ½bh, trapezoid A = ½(b₁+b₂)h; prism/cylinder V = Bh, pyramid/cone V = ⅓Bh, sphere V = (4/3)πr³ and SA = 4πr².