On-demand lessons are offered by topic. The price starts at $45 and depends on the number of students per session and the number and type of topics, as some topics could require more than an hour or multiple sessions. Please contact the teacher to get a quote for your needs and the time for the service.
Geometry Basics Topics
- Points, Lines, and Planes
- Segment Addition Postulate
- The Distance Formula
- The Midpoint Formula
- Partitioning a Segment
- Naming and Classifying Angles
- Angle Addition Postulate
- Angle Relationships (Adjacent, Vertical, Complementary, Supplementary, Linear Pair)
- Solving for Missing Measures using Algebra
- Special Relationships: Perpendicular and Angle Bisectors
- Constructions (Perpendicular bisectors, perpendicular line through a point on the line, perpendicular line through a point not on the line, line parallel to a given line through a given point, angle bisector, congruent angles)
Logic and Proof Topics
- Inductive Reasoning and Conjectures
- Compound Statements and Truth Tables
- Conditional Statements
- Related Conditionals (Inverse, Converse, Contrapositive)
- Biconditional Statements
- Venn Diagrams with Logic Statements
- Deductive Reasoning (Law of Detachment and Law of Syllogism)
- Properties of Equality (Addition, Subtraction, Multiplication, Division, Distributive, Substitution, Reflexive, Symmetric, Transitive)
- Algebraic Proofs
- Properties of Congruence (Reflexive, Symmetric, Transitive)
- Segment Proofs
- Angle Proofs
Parallel and Perpendicular Line Topics
- Parallel Lines, Parallel Planes, Skew Lines
- Lines and Angle Relationships: Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, Consecutive Interior Angles, Consecutive Exterior Angles
- Parallel Lines Cut by a Transversal: Solving for missing angles and using algebra to solve for missing angles.
- Proving Lines are Parallel: Using converses or algebraically.
- Parallel Line Proofs
- Slope Review: Find slope given a graph or two ordered pairs.
- Parallel and Perpendicular Lines: Using the slope formula to prove lines are parallel, perpendicular, or neither.
- Equations of Lines Review: Slope-Intercept Form, Standard Form, Vertical and Horizontal Lines
- Comparing Equations to determine parallel, perpendicular, or neither.
- The Point-Slope Formula: Writing linear equations given a point and slope or two points.
- Writing Parallel or Perpendicular Equations: Write an equation parallel or perpendicular to a given equation, passing through a specific point.
Congruent Triangles Topics
- Classifying Triangles by Sides and Angles
- Angles of Triangles: Triangle Angle Sum Theorem and Exterior Angle Theorem
- Isosceles and Equilateral Triangles
- Triangle Congruence: SSS and SAS
- Triangle Congruence: ASA and AAS
- Right Triangle Congruence: HL
- Mixed Review of Triangle Congruence
- Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Relationships in Triangles Topics
- Midsegments of Triangles (includes reinforcement of parallel lines)
- Perpendicular Bisectors and Angle Bisectors
- Circumcenter and Incenter
- Medians Centroid
- Altitudes and Orthocenter
- Naming and Identifying a Center
- Construction Centers of Triangles
- Centers of Triangles on the Coordinate Plane
- Inequalities in Triangles: Determine if three sides can form a triangle.
- Inequalities in Triangles: Find the range of the third side length of a triangle given two side lengths.
- Inequalities in Triangles: Order angles given sides and order sides given angles.
- Inequalities in Two Triangles (Hinge Theorem)
- Triangle Inequalities with Algebra
Similar Triangles Topics
- Ratio and Proportion: Includes extended ratio problems.
- Similar Figures: Identifying scale factors, and solving problems with similar figures using scale factors and proportions
- Proving Triangles Similar: Angle-Angle, Side-Side-Side, and Side-Angle-Side Similarity.
- Direct Similar Triangle Proofs
- Parallel Lines and Proportional Parts
- Parts of Similar Triangles: Altitudes, Angle Bisectors, and Medians
- Triangle Angle Bisector Theorem
Right Triangles and Trigonometry Topics
- Pythagorean Theorem and Applications
- Pythagorean Theorem Converse and Classifying Triangles
- Special Right Triangles: 45-45-90 and 30-60-90
- Similar Right Triangles
- Geometric Mean
- Trigonometric Ratios: Sine, Cosine, and Tangent
- Finding Missing Sides using Trigonometry
- Finding Missing Angles using Trigonometry
- Trigonometry Applications: Angle of Elevation and Angle of Depression
- Law of Sines
- Law of Cosines
- Solving Triangles
- Law of Sines and Law of Cosines Applications
Polygons and Quadrilaterals Topics
- Angles of Polygons
- Parallelograms
- Tests for Parallelograms in the Coordinate Plane: Using distance and slope formulas to prove parallelograms
- Parallelogram Proofs
- Rectangles
- Rhombi and Squares
- Quadrilaterals in the Coordinate Plane: Is it a parallelogram, rectangle, rhombus, or square?
- Non-Isosceles and Isosceles Trapezoids
- Midsegment of a Trapezoid
- Kites
Transformations Topics
- Translations (using coordinate and vector notation)
- Reflections (in the x-axis, y-axis, y = x, y = -x, and vertical and horizontal lines)
- Rotations (90°, 180°, and 270° rotations about the origin)
- Rotations (90°, 180°, and 270° rotations about any fixed point)
- Dilations (using the origin as the center of dilation)
- Dilations (using any fixed point as the center of dilation)
- Sequences of Transformations
- Symmetry (Line, Point, and Rotational)
Circles Topics
- Identifying Parts of Circles: Center, Radius, Chord, Diameter, Secant, Tangent, Central Angle, Inscribed Angle, Minor Arc, Major Arc, Semicircle
- Area and Circumference
- Central Angles
- Arc Lengths
- Congruent Chords and Arcs
- Inscribed Angles and Polygons
- Properties of Tangent Lines
- Arc and Angle Measures
- Segment Lengths
- Equation of a Circle (Graphing, identifying center, radius, circumference, area)
- Writing the Equation of a Circle in Standard Form (by completing the square)
Volume and Surface Area Topics
- Area of Plane Figures (Parallelograms, Rectangles, Squares, Triangles, Trapezoids, Circles)
- Area of Sectors of Circles
- Area of Composite Figures (including area of shaded regions)
- Classifying 3D Figures
- Surface Area of Prisms and Cylinders
- Surface Area of Pyramids and Cones
- Volume of Prisms and Cylinders
- Volume of Pyramids and Cones
- Volume and Surface Area of Spheres and Hemispheres
- Volume and Surface Area of Similar Solids
- Effects of Changing a Dimension on Volume and Surface Area
Probability Topics
- Introduction to Sets (Universal Set, Complement of a Set, Subsets, Union, Intersection - just basic!)
- Venn Diagrams
- Counting Outcomes (Fundamental Counting Principle)
- Theoretical Probability
- Experimental Probability
- Geometric Probability (Segments, Area, and Volume)
- Compound Probability: Independent Events
- Compound Probability: Dependent Events
- Conditional Probability
- Two-Way Tables
- Relative Frequency Two-Way Tables
- Probability with Two-Way Tables
- Permutations
- Combinations
- Probability with Permutations and Combinations
