Skill — Geometria sintetica.
Featured in chapters
08·09·14·15·16·33·38·42·44
Linked atoms
79 linked atoms.
08 Fondamenti di geometria euclidea
- A scheme for proofs
- Angles formed by parallel lines and a transversal
- Applying the scheme
- Base angles of the isosceles triangle
- Bisector, median and altitude
- Congruence criteria for right triangles
- Congruent opposite angles and parallelogram
- Diagonals that bisect each other and parallelogram
- Perpendicular bisector of a segment
- Problem — Congruence with the altitudes
- Proofs using parallelism
- Sum of the interior angles of a triangle
- The exterior angle is greater than the non-adjacent interior angles
- The first congruence criterion
- The five most frequent moves
- The hinge theorem
- The intercept theorem
- The parallelogram
- The perpendicular bisector as a locus
- The rectangle
- The rhombus and the bisecting diagonal
- The rhombus and the perpendicular diagonals
- The second congruence criterion
- The third congruence criterion
- Vertically opposite angles
- What a locus is
09 Metodo di lavoro — come risolvere un problema
- Example — carrying out the angle-bisector proof
- Example — finding the path, the isosceles triangle
- Example — reviewing the angle-bisector proof
- Example — understanding a geometry problem
- Worked problem — the bisector of the isosceles triangle
14 Equivalenza e teorema di Pitagora
- Equidecomposability of a triangle and a parallelogram
- Equivalence and equidecomposability
- Pythagoras’ theorem
- Rectangle of maximum area with fixed perimeter
15 Similitudine
- Euclid’s first theorem
- Euclid’s second theorem
- First similarity criterion
- Proof of Euclid’s theorems
- Similar triangles
- The Hermit Crab problem
16 Circonferenza
- Angle between a tangent and a chord
- Angle bisector theorem
- Angle inscribed in a semicircle
- Central angle and inscribed angle
- Centroid - concurrency of the medians
- Circumcentre - concurrency of the perpendicular bisectors
- Incentre - concurrency of the bisectors
- Intersecting chords
- Intersecting chords theorem
- Orthocentre - concurrency of the altitudes
- Proof of the central angle theorem
- Square with known diagonals
- Tangents from an external point
- The four notable points
33 Trigonometria dei triangoli
- Side of an inscribed regular polygon
- Solving a triangle with the law of cosines
- Trigonometry in right-angled triangles
38 Geometria sintetica nello spazio
- Dihedral angle between face and base
- Dihedral angle in the cube
- Euler’s formula
- Euler’s formula for the pentagonal prism
- Line perpendicular to a plane
- Prisms and parallelepipeds
- Sphere inscribed in a cone
- Thales’ theorem in space
- The cube - diagonal and hexagonal cross-section
- The dihedral angle and the normal section
- The five Platonic solids
- The pyramid
- Theorem of the three perpendiculars
42 Derivate
- Cylinder inscribed in a cone
- Rectangle inscribed in a semicircle
- Trapezium inscribed in a semicircle