Geometry

Geometry Topics covered by …and Math Tutoring

Lines
  • Angles in Measuring the Earth
  • Polygons and Polyhedra: Pyramid Architecture
  • Constructions: Telling Time with Shadows
The Nature of Deductive Reasoning
  • Conditional Statements
  • Definitions
  • Direct Proof
  • Indirect Proof
  • A Deductive System
  • Some Famous Theorems of Geometry
Lines and Angles
  • Number Operations and Equality
  • The Ruler and Distance
  • The Protractor and Angle Measure
  • Bisection
  • Complementary and Supplementary Angles
  • Linear Pairs and Vertical Angles
  • Perpendicular and Parallel Lines
Congruent Triangles
  • Coordinates and Distance
  • Polygons and Congruence
  • ASA and SAS Congruence
  • Congruence Proofs
  • Isosceles and Equilateral Triangles
  • SSS Congruence
  • Constructions
Inequalities
  • Properties of Inequality
  • The Exterior Angle Theorem
  • Triangle Side and Angle Inequalities
  • The Triangle Inequality Theorem
Parallel Lines
  • Line Symmetry
  • Proving Lines Parallel
  • The Parallel Postulate
  • Parallel Lines and Angles
  • The Angles of a Triangle
  • Perimeters and Areas of Similar Figures
Quadrilaterals
  • Quadrilaterals
  • Parallelogram and Point Symmetry
  • More on Parallelograms
  • Rectangles, Rhombuses, and Squares
  • Trapezoids
  • The Midsegment Theorem
Transformations
  • Transformations and Symmetry
  • Reflections
  • Isometries and Congruence
  • Transformations and Symmetries
Area
Squares and Rectangles
Triangles
Parallelograms and Trapezoids
The Pythagorean Theorem
Similarity
  • Ratio and Proportion
  • Similar Figures
  • The Side-Splitter Theorem
  • The AA Similarity Theorem
  • Proportions and Dilations
  • Perimeters and Areas of Similar Polygons
The Right Triangle
  • Proportions in a Right Triangle
  • The Pythagorean Theorem Revisited
  • Isosceles and 30°-60° Right Triangles
  • The Tangent Ratio
  • The Sine and Cosine Ratios
  • Slope
  • The Laws of Sines and Cosines
Circles
  • Circles, Radii and Chords
  • Tangents
  • Central Angles and Arcs
  • Inscribed Angles
  • Secant Angles
  • Tangent Segments and Intersecting Chords
The Concurrence Theorems
  • Triangles and Circles
  • Cyclic Quadrilaterals
  • Incircles
  • The Centroid of a Triangle
  • Ceva’s Theorem
  • Napoleon’s Discovery and Other Surprises
Regular Polygons and the Circle
  • Regular Polygons
  • The Perimeter of a Regular Polygon
  • The Area of a Regular Polygon
  • From Polygons to Pi
  • The Area of a Circle
  • Sectors and Arcs
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