LVL: FREE 20H_EST Level 5

Geometry Foundations

Geometry is more than just shapes; it is the study of spatial relationships. This path guides you through lines, angles, polygons, and circles, moving into 3D polyhedra and revolution solids, and finally introducing coordinate geometry and vectors.

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Curriculum

1Part 1

Theory

Points, lines, rays, and line segments

Types of triangles and the sum of angles

3Part 2

Theory

Congruence criteria for triangles

4General Concepts

Theory

Similarity criteria for triangles

Theory

Right triangles and the Pythagorean Theorem

Theory

Quadrilaterals: parallelogram, rectangle, rhombus, square

Theory

Trapezoid and its properties

5Part 3

Theory

Perimeter and area of basic figures

6General Concepts

Theory

Radius, chord, diameter, tangent, and secant

Theory

Circumference and area of a circle

Theory

Central and inscribed angles

Theory

Relative positions of lines (intersecting, parallel, skew)

7Part 4

Theory

Perpendicularity of a line and a plane

8General Concepts

Theory

Dihedral angles

Theory

Prisms and parallelepipeds (surface area and volume)

Theory

Pyramids (surface area and volume)

Theory

Cylinder (properties, area, volume)

9Part 5

Theory

Cone (properties, area, volume)

10General Concepts

Theory

Sphere and ball (properties, area, volume)

Theory

Distance between two points

Theory

Midpoint coordinates

Theory

Slope and intercept

11Part 6

Theory

Equation of a line

12General Concepts

Theory

Equation of a circle

Theory

Geometric meaning of intersecting graphs

Theory

Concept of a vector, magnitude, and direction

Theory

Vector addition and subtraction (triangle and parallelogram rules)

13Part 7

Theory

Scalar multiplication of a vector

14General Concepts

Theory

Geometry Foundations

Curriculum

1Part 1

Points, lines, rays, and line segments

2General Concepts

Types of angles (acute, right, obtuse, straight)

Adjacent and vertical angles

Parallel and perpendicular lines. Angles formed by a transversal

Types of triangles and the sum of angles

3Part 2

Congruence criteria for triangles

4General Concepts

Similarity criteria for triangles

Right triangles and the Pythagorean Theorem

Quadrilaterals: parallelogram, rectangle, rhombus, square

Trapezoid and its properties

5Part 3

Perimeter and area of basic figures

6General Concepts

Radius, chord, diameter, tangent, and secant

Circumference and area of a circle

Central and inscribed angles

Relative positions of lines (intersecting, parallel, skew)

7Part 4

Perpendicularity of a line and a plane

8General Concepts

Dihedral angles

Prisms and parallelepipeds (surface area and volume)

Pyramids (surface area and volume)

Cylinder (properties, area, volume)

9Part 5

Cone (properties, area, volume)

10General Concepts

Sphere and ball (properties, area, volume)

Distance between two points

Midpoint coordinates

Slope and intercept

11Part 6

Equation of a line

12General Concepts

Equation of a circle

Geometric meaning of intersecting graphs

Concept of a vector, magnitude, and direction

Vector addition and subtraction (triangle and parallelogram rules)

13Part 7

Scalar multiplication of a vector

14General Concepts

Dot product of vectors (geometric and coordinate meaning)