Geometry
Demo1. Right & Oblique
Comparison of right and oblique prisms, and differences in determining their surface area, height and volume.
2 5 1 1
Lesson multimedia content (1)
The surface area of a right prism
2. Basic Concepts
The building blocks of geometry, rays and line segments, and the definition of finite and infinite sets.
3 6 1 1
Lesson multimedia content (1)
Finite or infinite?
3. Position report
Determination of the relative positions of spatial elements.
3 6 1 1
Lesson multimedia content (1)
The mutual position of the elements in space
4. Angles in Space
Angles between lines, planes, and lines and planes, perpendicularity, and determination of angles in space.
3 5 1 1
Lesson multimedia content (1)
The angle between two planes
5. Near and Far
Distances between points, lines and planes, units of measurement, and determination of the shortest distance.
3 4 1 1
Lesson multimedia content (1)
Use of units of measurement
6. Locus in Geometry
Determination of specially positioned points and sets of points in the plane and in space.
2 3 1 1
Lesson multimedia content (1)
Locus of points in space
7. Vectors
Vectors, their magnitude and direction, opposite vectors, and the sum and difference of vectors.
3 7 1 1
Lesson multimedia content (1)
Multiplying a vector by a scalar
8. Planar Transformations
Basics of point transformations and congruence transformations: translation, rotation, line reflection and point reflection.
2 5 1 1
Lesson multimedia content (1)
Planar transformations
9. Translation
Vector definition of translation and its distance-, angle- and orientation-preserving properties.
3 5 1 1
Lesson multimedia content (1)
Translation
10. Reflection
Point and line reflection, fixed points, invariant lines, and the properties of the transformations.
3 7 1 1
Lesson multimedia content (1)
Reflection about a line in space
11. Similarity
Similarity transformation, scale factor, reduction and enlargement, and ratios of length, area and volume.
3 7 1 1
Lesson multimedia content (1)
The similarity transformation
12. The Plane as a Mirror
Reflection about a plane, fixed and invariant shapes, and the geometric properties of a plane mirror.
3 6 1 1
Lesson multimedia content (1)
Reflection about a plane in space
13. Rotation about a Point
Rotation about a point, direction, angle, fixed point, and identity transformations.
3 5 1 1
Lesson multimedia content (1)
Rotation about a point
14. Rotation in Space
Rotation about a line in space, rotation axis, fixed points, direction, and congruence properties.
3 6 1 1
Lesson multimedia content (1)
Rotation about a line in space
15. Pythagorean Theorem
Pythagorean theorem, relations between sides of right triangles, proof, and Pythagorean triples.
2 6 1 1
Lesson multimedia content (1)
Illustration of the Pythagorean theorem
16. Thales' Theorem
Thales’ theorem, its proof, inscribed angle subtended by a diameter, and applications of the theorem.
2 6 1 1
Lesson multimedia content (1)
Application of Thales’ theorem
17. Theorems abuot (Tri)Angles
Altitude theorem, leg theorem, intercept theorem, related proportions, and the concept of the geometric mean.
3 7 1 1
Lesson multimedia content (1)
The theorem of parallel intercepting line segments
18. Trigonometry
Trigonometric relations in right triangles: sine, cosine, tangent and cotangent functions.
2 6 1 1
Lesson multimedia content (1)
Representation of the sine and cosine trigonometric functions
19. Laws of Sines and Cosines
Application of the laws of sines and cosines to determine sides and angles of any triangles.
2 6 1 1
Lesson multimedia content (1)
Treasure hunt exercise
20. Quadrilaterals
Classification and properties of quadrilaterals: trapezium, parallelogram, rhombus, rectangle, deltoid and square.
3 6 1 1
Lesson multimedia content (1)
Perimeter and area of quadrilaterals
21. Outside & Inside
Properties of cyclic and tangential quadrilaterals and the related geometric theorems.
2 5 1 1
Lesson multimedia content (1)
Constructing the circumcircle of a quadrilateral
22. Polygons
Characteristics of polygons, diagonals, interior and exterior angles, and properties of regular polygons.
2 5 1 1
Lesson multimedia content (1)
The area of a regular polygon
23. Polyhedra
Polyhedra, Euler’s polyhedral formula, and the characteristics of regular solids.
3 6 1 1
Lesson multimedia content (1)
Solving a math problem: Octahedron
24. Prisms
Definition and parts of prisms, and calculation of their surface area and volume.
2 5 1 1
Lesson multimedia content (1)
Derivation of a prism
25. On Quadrilateral Bases
Calculation of surface area and volume of special right prisms with quadrilateral bases, with a practical example.
2 5 1 1
Lesson multimedia content (1)
The square prism
26. From Column to Cube
Properties, surface area and volume of square prisms and cubes, with a practical Rubik’s Cube example.
3 6 1 1
Lesson multimedia content (1)
The volume of a cube
27. Pyramid
Definition and parts of pyramids, their derivation, right and oblique pyramids, surface area and volume formulas.
3 8 1 1
Lesson multimedia content (1)
The volume of a pyramid
28. Truncated Pyramid
Definition and parts of truncated pyramids, surface area and volume, and application of similarity rules.
2 6 1 1
Lesson multimedia content (1)
The surface area of a truncated pyramid
29. Circles
Basic circle concepts: circumference, radius, diameter, tangent, secant, chord, and calculation of circumference and area.
2 6 1 1
Lesson multimedia content (1)
The circumference and area of the circle
30. Inside the Circle
Parts of a circle: disc, annulus, sector, segment and semicircle, and determination of their areas.
2 5 1 1
Lesson multimedia content (1)
Relationships in the circle
31. Angles in the Circle
Central and inscribed angles, their corresponding arcs, and the relations between them.
2 9 1 1
Lesson multimedia content (1)
Measuring angles
32. Spheres
Characteristics of spheres and spherical surfaces, radius, diameter, and determination of surface area and volume.
2 5 1 1
Lesson multimedia content (1)
The surface area of a sphere
33. Is the Earth a Sphere?
Geometric relations between the sphere and Earth, geographical coordinates, latitude and longitude.
2 5 1 1
Lesson multimedia content (1)
The volume of a sphere
34. (Circular) Cylinders
Definition of cylinders, types and parts of circular cylinders, and formulas for surface area and volume.
2 7 1 1
Lesson multimedia content (1)
The circular cylinder
35. Cones
Parts of cones and cones of revolution: generator, lateral surface, base, and determination of surface area and volume.
3 7 1 1
Lesson multimedia content (1)
Volume of a circular cone
36. Cones of Revolution
Geometric properties of cones of revolution generated by rotating axially symmetric plane figures.
3 8 1 1
Lesson multimedia content (1)
The surface area and volume of nested cones
37. Cross Sections of a Cone
Plane sections of cones of revolution: circle, ellipse, parabola and hyperbola, plus truncated-cone derivation and surface area.
3 7 1 1
Lesson multimedia content (1)
The volume of a truncated cone
38. "Spun" around
Solids of revolution generated by rotating plane figures around a symmetry axis, and examination of their volumes.
3 6 1 1
Lesson multimedia content (1)
How heavy is the ball?
39. Inscribed Solids
Archimedes’ theorem, and the concept and characteristics of dual solids.
3 7 1 1
Lesson multimedia content (1)
Spheres inscribed in a cuboid
40. A Solid in a Solid
Joined geometric solids, Platonic solids, and the stellated octahedron.
3 6 1 1
Lesson multimedia content (1)
A sphere inscribed in a cone
| 40 topics | |
| 102 slajd | |
| 1 selftest | |
| 39 test | |
| 164 obraz | |
| 40 Wideo 3D | |
| Zobacz wszystkie strony |
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