# 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
##### 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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