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Geometry II
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.
Some of the topics and problems that are studied in this course include:
Perpendicular lines and planes in space.
Parallel lines in a plane. The sum of the angles of the triangle. The triangle median concurrence theorem.
Quadrilaterals in a plane. Parallelogram, trapezoid, rhombus, rectangle, and square.
Right triangles. The 30-60-90 and 45-45-90 triangles.
Parallel lines and planes. Dihedral angles. Perpendicular planes. Projections.
Polygonal regions and their areas. Areas of triangles and quadrilaterals.
Pythagorean theorem.
Similarity. Proportionality. Similar triangles. Triangle similarity theorems: AA, SAS, and SSS.
Similarities in right triangles. Areas of similar triangles.
Circles and Spheres. Tangent lines and planes. Chords, secants, arcs. Inscribed angles, intercepted arcs and their degree measurements. Measures of angles and segments formed by intersecting tangents, secants and chords.
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