高校幾何学の旅 - パート 2

This course is designed to provide comprehensive coverage of the concepts in the High School Geometry course. This is part 2 of the year-long course and it is recommended that students have taken part 1.  During this course, we will get through 4 chapters. Students will apply previous mathematical experiences to solve real-world problems. 

Chapter 4: Triangles and Congruence
This chapter dives into the fundamental properties of triangles, exploring concepts like triangle classification, congruence criteria (SSS, SAS, ASA, AAS), and proofs involving triangle congruence. Students will learn to apply these principles to solve geometric problems and prove geometric relationships.

Chapter 5: Relationships in Triangles
In this chapter, students deepen their understanding of triangle relationships, including angle bisectors, medians, altitudes, and inequalities within triangles. They will explore how these relationships contribute to triangle properties and solve problems involving triangle inequalities and indirect proofs.

Chapter 6: Quadrilaterals
Students will study various types of quadrilaterals, focusing on their properties, classifications, and special characteristics such as parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. They will learn to apply coordinate geometry to prove properties of quadrilaterals and solve problems related to their angles, sides, and diagonals.

Chapter 7: Proportions and Similarity
This chapter introduces the concept of similarity in geometric figures, particularly focusing on similar polygons and triangles. Students will explore criteria for similarity (AA similarity, SSS similarity, SAS similarity) and how to use proportions and scale factors to solve problems involving similar figures. They will also investigate applications of similarity in real-world contexts and geometric constructions.

By the end of these 4 chapters, students will have gained a thorough understanding of fundamental geometric concepts including triangle properties and congruence criteria, relationships within triangles such as bisectors and inequalities, properties and classifications of quadrilaterals, and the principles of similarity in polygons and triangles. They will be proficient in applying geometric proofs and solving complex problems involving angles, sides, and proportions. Additionally, students will have developed critical thinking skills through logical reasoning, and they will be able to confidently apply geometric principles to real-world situations.