 |
|
|
| |
|
|
|
| |
|
Geometry I
In this course, students learn the basic definitions, postulates, and theorems of geometry and application of this knowledge to problem solving. The stress of this course is done on three key elements of geometry:
1. Logical reasoning in geometry.
2. Direct and indirect proofs.
3. Problem solving on the base of theory and logical reasoning.
Concepts introduction and problem solving formed an integral part of each class session. Student learned extensively from and by examples, and a variety of instructional methods were used to enhance students' problem-solving abilities. Students tackled many complicated problems using direct and indirect proofs in deductive reasoning approach. Some of the topics and problems that were studied in this course included:
Common Sense vs. Exact Reasoning.
Sets, real numbers, and lines.
Betweenness, segments and rays.
Intersection of planes and plane separation.
Angles and triangles.
Theorems, hypothesis, and conclusion. Writing up proofs.
Congruent triangles.
SAS, ASA, and SSS postulates and theorems for congruent triangles.
Quadrilaterals, medians, and bisectors.
Geometric inequalities for segments and angles.
Inequalities in triangle.
Perpendicular and parallel lines and planes in space.
Quadrilaterals in a plane. Rhombus, rectangle, and square
|
|
|
|
|
|