Syllabus:
We will cover these topics, in this order:
1. Basics of Geometry
This chapter will introduce you to the basic elements of geometry, including points, lines, planes, and angles. Midpoints and line segments are also covered.
2. Reasoning and Proof
An introduction to the concepts surrounding proofs, including inductive reasoning, conditional statements, and properties of congruence.
3. Parallel and Perpendicular Lines
Properties of parallel and perpendicular lines, including some 2 column proofs and proof of algebraic equations.
4. Triangles and Congruence
Explore the properties of triangles, especially their angles. Learn different ways to determine congruence. Isosoceles and equilateral triangles are also covered.
5. Relationships with Triangles
Points of concurrency using medians, altitudes and perpendicular bisectors.
6. Similarity
An overview of ratios and proportions and the concept of similarity as it applies to polygons, quadrilaterals and triangles. Dilations are included in this section.
7. Polygons and Quadrilaterals
Properties of polygons and quadrilaterals, including parallelograms, rhomboid, rectangles, squares, kites, and trapezoids.
8. Right Triangle Trigonometry
The Pythagorean theorem and its converse and an introduction to trigonometry ratios, the Law of Sines and Cosines.
9. Perimeter and Area
One and Two dimensional measurements of triangles, quadrilaterals, polygons, and circles.
10. Surface Area and Volume
Two and Three dimensional measurements of 3D figures.
11. Rigid Transformations
Symmetry, followed by translations, reflections, and rotations.
12. Circles
Parts of a circle and properties of tangent lines, arcs, inscribed angles, chords, angles, and segments formed by chords, tangents, and secants. Equations and graphs of circles are also explored.
13. Probability
Geometric probability
1. Basics of Geometry
This chapter will introduce you to the basic elements of geometry, including points, lines, planes, and angles. Midpoints and line segments are also covered.
2. Reasoning and Proof
An introduction to the concepts surrounding proofs, including inductive reasoning, conditional statements, and properties of congruence.
3. Parallel and Perpendicular Lines
Properties of parallel and perpendicular lines, including some 2 column proofs and proof of algebraic equations.
4. Triangles and Congruence
Explore the properties of triangles, especially their angles. Learn different ways to determine congruence. Isosoceles and equilateral triangles are also covered.
5. Relationships with Triangles
Points of concurrency using medians, altitudes and perpendicular bisectors.
6. Similarity
An overview of ratios and proportions and the concept of similarity as it applies to polygons, quadrilaterals and triangles. Dilations are included in this section.
7. Polygons and Quadrilaterals
Properties of polygons and quadrilaterals, including parallelograms, rhomboid, rectangles, squares, kites, and trapezoids.
8. Right Triangle Trigonometry
The Pythagorean theorem and its converse and an introduction to trigonometry ratios, the Law of Sines and Cosines.
9. Perimeter and Area
One and Two dimensional measurements of triangles, quadrilaterals, polygons, and circles.
10. Surface Area and Volume
Two and Three dimensional measurements of 3D figures.
11. Rigid Transformations
Symmetry, followed by translations, reflections, and rotations.
12. Circles
Parts of a circle and properties of tangent lines, arcs, inscribed angles, chords, angles, and segments formed by chords, tangents, and secants. Equations and graphs of circles are also explored.
13. Probability
Geometric probability