Geometry
(two semester course)
Geometry is the third theoretical course in Classic Math School’s Enrichment Program, and intended for students from 7th to 10th grade. The course prerequisites include fluency in making and solving linear and quadratic equations and inequalities (Algebra I). This course generally covers the same topics as most of Geometry courses around the country, but in a greater depth and with provided/required proofs.
Concepts introduction and problem solving formed an integral part of each class session. Students learn extensively from and by examples, and through problem discussions. A variety of instructional methods are used to enhance students' problem-solving abilities. Students tackle many complicated problems using direct and indirect proofs in deductive reasoning approach.
Some of the topics and problems that are studied in Geometry course may include:
Common Sense vs. Exact Reasoning.
Undefined Basic Geometric Terms: Point, Line, Plane.
Inductive and Deductive Reasoning.
Postulates and Definitions. Theorems. Predicates, Converses, Inverses, Contrapositives, Biconditionals. Writing up Proofs.
Segments, Rays, Angles and their Proper Notations.
Collinearity, Betweenness, Coplanarity.
Congruency of Segments, Segment Addition Postulate. Congruency of Angles, Angles Addition Postulate. Supplementary, Complementary, Adjacent, Vertical Angles.
Congruent Triangles. SAS, ASA, SSS, AAS Postulates and Theorems. CPCTC.
Triangle Medians, Altitudes and Angle Bisectors. Isosceles and Equilateral Triangles. Perpendicular Bisectors.
Exterior Angle Theorem.
Perpendicular and Parallel Lines and Planes in Space.
Parallel Lines in a Plane. The Sum of Interior Angles of a Triangle. The Triangle Inequalities.
Quadrilaterals: Parallelogram, Trapezoid, Rhombus, Kite, Rectangle, and Square. Properties of Special Quadrilaterals and their Relationships.
Right triangles. The 30-60-90 and 45-45-90 triangles.
Pythagorean Theorem and its Converse.
Polygonal Regions and their Areas. Areas of Triangles and Quadrilaterals.
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.
Basic Geometric Constructions. Locus. Concurrence Theorems.