Enrichment - Grade 9-10 Math: Geometry 班

Textbook: Schuam's Geometry
Geometry - Grade 9 or 10 and have to completed Algebra I
适合已修完代数1的学生，此课设立为几何加强班

• 该课主要学习线段、三角形、四边形、圆形知识并进一步用于全等和相似形. 此课策重于证明题和推理题，在此课堂里可以学到的证明和推理是在美国学校里学被突略的内容。
• 此课还将包括所有几何必学内容：长度、周长、面积、圆周、立体图形面积和体积会通过做大量的证明题和运算题来提高解题技巧和实际应用能力。

• This class will cover congruence and similarity, as well as properties of lines, triangles, quadrilaterals, and circles. The class will mostly concentrate on formulating proofs and abstract thinking, which are generally not primary concentrations in public school geometry classes.
• Students will develop their ability to write proofs, to strengthen their abstract thinking, and to apply their skills in solving problems using length, perimeter, area, circumference, surface area, and volume to the real world.

Math Geometry Class Teaching Outline

Text book Schaum’s Outlines Geometry (Third Edition)

1. Introducing Geometry – Point, Lines, Planes, Midpoint, Bisector, Angles, and Triangles, Line Segments, Circles, Angles, Triangle, Pairs of Angles.
2. Methods of Proof – Prof by Deductive Reasoning, Postulates (Assumptions), Basic Angle Theorems, Determining the Hypothesis and Conclusion, Proving a Theorem.
3. Parallel Lines, Distances, and Angle Sums – Parallel Lines, Distances, Sum of the Measures of the Angles of a Triangle, Sum of the Measures of the Angles of a Polygon, Two New Congruency Theorems.
4. Congruent Triangles – Congruent Triangles, Isosceles and Equilateral Triangles, Right Triangles.
5. Parallelogram, Trapezoids, Medians, and Midpoints – Trapezoids, Parallelograms, and Special Parallelograms: Rectangle, Rhombus, Square, Three or More Parallels: Medians and Midpoints.
6. Similarity – Ratios, Proportions, Proportional Segments, similar Triangles, Extending a Basic Proportion Principle, Proving Equal Products of Lengths of Segments, Segments Intersecting Inside and Outside a Circle, Mean Proportional in a Right Triangle, Pythagorean Theorem, and Special Right Triangles.
7. Circles – The Circle; Circle Relationships, Tangents, Measurement of Angles and Arcs in a Circle.
8. Areas – Area of a Rectangle and of a square, Area of a Parallelogram, Area of a Triangle, Area of a Trapezoid, Area of a Rhombus, Polygons of the Same Size or Shape, Comparing Areas of Similar Polygons, Areas in Analytic Geometry.
9. Regular Polygons and the Circle – Regular Polygons, Relationships of Segments in Regular Polygons of 3, 4, and 6 Sides, Area of a Regular Polygon, Ratios of Segments and Areas of Regular Polygons, Circumference and Area of a Circle Length of a Arc; Area of a Sector and a Segment, Areas of Combination Figures.