高校幾何学をマスターする: 基礎から証明まで

My class, "Mastering High School Geometry: From Basics to Proofs," is designed to help students master the fundamental concepts of geometry. We will cover a wide range of topics, from basic shapes and angles to more advanced topics like proofs and transformations.
Geometry Tutoring Syllabus

Course Duration: 12 Weeks
Objective: Develop a strong foundation in geometric concepts, logical reasoning, and problem-solving skills.

Week 1: Basics of Geometry

. Points, lines, planes, and angles
. Types of angles (acute, right, obtuse, straight)
. Measuring and classifying angles
. Segment and angle bisectors
. Midpoints and distance formula

Week 2: Reasoning and Proofs

. Inductive vs. deductive reasoning
. Conditional statements and their converses
. Properties of equality and congruence
. Writing two-column proofs and paragraph proofs

Week 3: Parallel and Perpendicular Lines

. Properties of parallel lines and transversals
. Identifying corresponding, alternate interior, and same-side interior angles
. Slope and equations of parallel and perpendicular lines
. Proving lines are parallel or perpendicular

Week 4: Transformations

. Reflections, translations, rotations, and dilations
. Properties of rigid and non-rigid transformations
. Compositions of transformations
. Symmetry (line and rotational)

Week 5: Congruent Triangles

. Triangle congruence criteria (SSS, SAS, ASA, AAS, HL)
. Using congruence to prove parts of triangles are congruent
. Isosceles and equilateral triangle properties
. Overlapping triangles in proofs

Week 6: Relationships Within Triangles

. Midsegments and their properties
. Perpendicular bisectors, angle bisectors, medians, and altitudes
. Triangle inequalities
. Hinge Theorem
Week 7: Quadrilaterals and Other Polygons

. Properties of parallelograms, rectangles, rhombuses, squares, and trapezoids
. Conditions for proving quadrilateral types
. Sum of interior and exterior angles in polygons

Week 8: Similarity

. Proportions and similarity ratios
. Triangle similarity (AA, SSS, SAS)
. Proportional parts in triangles
. Using similarity to find missing lengths

Week 9: Right Triangles and Trigonometry

. Pythagorean Theorem and its applications
. Special right triangles (30°-60°-90° and 45°-45°-90°)
. Trigonometric ratios (sine, cosine, tangent)
. Solving right triangles using trig functions

Week 10: Circles

. Parts of a circle (radius, chord, diameter, tangent, secant)
. Arc measures and central angles
. Inscribed angles and their properties
. Equations of circles in coordinate geometry

Week 11: Circumference and Area

. Circumference and arc length
. Area of circles and sectors
. Area of composite figures

Week 12: Surface Area and Volume

. Surface area and volume of prisms, cylinders, pyramids, cones, and spheres
. Applying the formulas to real-world problems
. Effects of changing dimensions on surface area and volume