Zeihen RMHS 605
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  • Algebra 2
    • Unit 1: Rational Numbers and Polynomial Expressions >
      • Unit 1 Segment 1: Structure in Expressions >
        • Lesson 1-1 Properties of Real Numbers
        • Lesson 1-2 Algebraic Expressions
        • Algebra 1 Ch 7 Lesson: Rules of Exponents
        • Lesson 6-1 Polynomial Functions
        • Lesson 6-1 Exploring Polynomial Functions
        • Lesson 1-3 Solving Equations
        • Lesson 6-1 Multiplying Polynomials
        • Lesson 5-4 Factoring Techniques
        • Other Factoring Techniques
        • 5-5 Quadratic Graphing and their Zero's
        • 6-2 Polynomials and their Linear Factors
        • 6-2 The Factor Theorem, Zeros, and Multiplicity
        • 6-3 Dividing Polynomials, Synthetic Division, Remainder Theorem
        • 6-3 Synthetic Divsion
      • Unit 1 Segment 2: Polynomial Arithmetic >
        • Lesson 5-8 The Quadratic Formula
        • 6-4 Solving Polynomial Equations with Quadratic Techniques
        • 6-5 Theorems about Roots of Polynomial Equations
      • Unit 1 Segment 3: Binomial Theorem & Pascal's Triangle >
        • Lesson 6-7 Permutations
        • Lesson 6-7 Combinations
        • 6-8 Pascal's Triangle and the Binomial Expansion Theorem
    • Unit 2: Equations and Their Graphs >
      • Unit 2 Segment 1: Reasoning With Equations & Inequalities >
        • Lesson 9-3 Graphing Rational Equations
        • Lesson 9-4 Solving Simple Rational Equations
        • Lesson 2-5 Graphing Absolute Value Functions
        • Lesson 1-5 Solving Absolute Value Equations
      • Unit 2 Segment 2: Solve Equations Graphically
    • Unit 3: Complex Numbers >
      • Unit 3 Segment 1: Complex Number Operations >
        • 5-6 Complex Numbers and Conujates
        • 5-6 Graphing Complex Numbers, Absolute Value and Conjugates
      • Unit 3 Segment 2: Complex Numbers in Quadratic Equations
    • Unit 4: Trigonometric Functions >
      • Unit 4 Segment 1: The Unit Circle, Radians, and Degrees >
        • Lesson on Special Right Triangles
        • Basic Trig Ratios Reviewed
        • Ferris Wheel Exploration Day 1
        • Ferris Wheel Exploration Day 2
        • Lesson 13-2 Angles and the Unit Circle
        • Lesson 13-3 Radian Measure
        • Lesson 13-2 The Unit Circle
      • Unit 4 Segment 2: Graphing Trigonometric Functions >
        • Lesson 13-1 Periodic Functions
        • Lesson 13-4 Sine Graphs
        • Cosine Graphs
        • Tangent Graphs
      • Unit 4 Segment 3: Proving Trigonometric Identities >
        • Lesson 14-1 Trigonometric Identities
    • Unit 5: Modeling With Functions >
      • Unit 5 Segment 1: Graphing Functions
      • Unit 5 Segment 2: Interpreting Functions >
        • Lesson 1-3 Using Equations to Model Problems
        • Lesson 1-4 Using Inequalities to Model Problems
      • Unit 5 Segment 3: Comparing Functions
      • Unit 5 Segment 4: Functions and Their Inverses >
        • Lesson 7-7 Inverse and Functions
        • Lesson 8-3 Logarithm and Inverses of Exponential Functions
    • Unit 6: Inferences and Conclusions From Data >
      • Unit 6 Segment 1: Standard Deviation, Mean, & Normal Distribution
      • Unit 6 Segment 2: Random Process & Empirical Versus Theoretical
      • Unit 6 Segment 3: Sample Surveys, Experiments and Observational Studies
  • Alg 2 Honors SS Blog
  • Geometry
    • Unit 1 Foundations of Geometry >
      • Unit 1 Segment 1: Basic Geometric Figures >
        • Lesson 1-3 Points, Lines & Planes
        • Lesson 1-4 Segments, Rays, Parallel Lines and Planes
        • Lesson 1-5 Measuring Segments
        • Lesson 1-6 Measuring Angles
      • Unit 1 Segment 2: Constructions >
        • Lesson 1-7 Basic Constructions
        • Making shapes with Constructions
      • Unit 1 Segment 3: Deductive Reasoning >
        • Lesson 1-1 Inductive Reasoning, "Patterns!"
        • Lesson 2-1 Conditional Statements
        • Lesson 2-2 Bi-Conditional Statements
        • Lesson 2-3 Deductive Reasoning "Logic"
        • Lesson 2-4 Reasoning in Algebra
        • Lesson 2-5 Vertical, Complementary, and Supplementary Pairs and AAP
        • Lesson 5-4 Negation with Inverse and Contrapositive Statements
    • Unit 2 Parallel Lines and Transformations >
      • Unit 2 Segment 1: Transformations >
        • Lesson 9-1 Transformations
        • Lesson 9-2 Reflections
        • Lesson 9-3 Rotations
      • Unit 2 Segment 2: Properties of Parallel Lines and Proving Lines are Parallel >
        • Lesson 3-1 Angles Formed by Parallel Lines
        • Lesson 3-2 Proving Lines Parallel
        • Lesson 3-3 Parallel and Perpendicular Lines
        • Lesson 3-8 Constructing Parallel and Perpendicular Lines
        • Writing Proofs involving Parallel Lines and Triangles
      • Unit 2 Segment 3: Triangle Angle Sum Theorem >
        • Lesson 3-4 Theorems about Angles in Triangles
        • Lesson 3-5 Interior Angles in Polygons
        • Lesson 3-5 Polygons and Shapes
    • Unit 3 Congruence >
      • Unit 3 Segment 1: Triangle Congruence Theorem with Transformations >
        • Lesson 4-1 Congruent Polygons and Transfomations
        • Lesson 4-2 Congruent Triangles SSS SAS
        • Lesson 4-3 Congruent Triangles ASA AAS
        • Lesson 4-4 Using Congruent Triangles & CPCTC
        • Lesson 4-5 Isosceles and Equilateral Triangles
        • Lesson 4-6 Congruence in Right Triangles HL Theorem
        • Lesson 4-7 Using Corresponding Parts of Congruent Triangles
      • Unit 3 Segment 2: Using Congruent Triangles to Prove Properties of Quadrilaterals >
        • Lesson 6-1 Classifying Quadrilaterals
        • Lesson 6-2 Properties of Parallelograms
        • Lesson 6-3 Proving that a Quadrilateral is a Parallelogram
        • Lesson 6-4 Special Parallelograms
        • Lesson 6-5 Trapezoids and Kites
      • Unit 3 Segment 3: Develop Area by Building Shapes from Triangles and Rectangles >
        • Lesson 10-1 Area of Parallelograms and Triangles
        • Lesson 10-2 Area of Trapezoids, Rhombuses, and Kites
        • Lesson 10-3 Area of Regular Polygons
    • Unit 4 Coordinate Geometry >
      • Unit 4 Segment 1: Introduction to Coordinate Geometry >
        • Lesson 1-8 Coordinate Plane, Distance, and Midpoint Formulas
      • Unit 4 Segment 4: Slope of Parallel and Perpendicular Lines >
        • Lesson 3-6 Slopes and Lines in the Coordinate Plane
        • Lesson 3-7 Slopes of Parallel and Perpendicular Lines
      • Unit 4 Segment 2: Pythagorean Theorem and its Applications >
        • Lesson 5-5 Inequalities in Triangles
        • Lesson 8-1 The Pythagorean Theorem
        • Lesson 1-9 Perimeter, Circumference, and Area
        • Lesson 6-6 Placing Figures in the Coordinate Plane
        • Lesson 6-7 Proofs Using Coordinate Geometry
      • Unit 4 Segment 3: Derive the Equation of a Circle Using Distance Formula & Pythagorean Theorem >
        • Lesson 12-5 Equation of a Circle
      • Unit 4 Segment 5: Parabolas >
        • Parabolas Using Focus and Directrix
    • Unit 5 Similarity >
      • Unit 5 Segment 1: Definition of Similarity using Dilations >
        • Lesson 7-1 Ratios and Proportions
        • Lesson 9-5 Dilations
        • Lesson 7-2 Similar Polygons
        • Lesson 7-3 Proving Triangles Similar
      • Unit 5 Segment 2: Applications of Similarity in Triangles >
        • Lesson 7-5 Proportions in Triangles
        • Lesson 5-1 Midsegments in Triangles
        • Lesson 5-3 Concurrent Lines, Medians and Altitudes
        • Lesson 8-6 Vectors or scalar multiplication
    • Unit 6 Trigonometry >
      • Unit 6 Segment 1: Special Right Triangles and the Pythagorean Theorem >
        • Lesson 8-2 Special Right Triangles
        • Lesson 8-2 Special Right Triangles
      • Unit 6 Segment 2: Trigonometry Ratios and Similarity >
        • Lesson 8- 3 Tangent in Right Triangles
        • Lesson 8-4 Cosine
        • SOHCAHTOA
        • Lesson 8-3 The Tangent Ratio
        • Lesson 8-4 Sine and Cosine Ratios
      • Unit 6 Segment 3: Trigonometry Identities >
        • Lesson 8-5 Trig Identities, Angles of Elevation and Depression
      • Unit 6 Segment 4: Laws of Sines and Cosines and Applications >
        • Lesson on Law of Sines
        • Lesson on Law of Cosines
        • Lesson 10-5 Area of Regular Polygons and Trigonometry
    • Unit 7 Circles >
      • Unit 7 Segment 1: Introduction to Circles and Similarity
      • Unit 7 Segment 2: Angle Measures and Segment Lengths in Circles >
        • Lesson 10-6 Circles and Arcs
        • Lesson 12-2 Chords, Arcs, and Angles
        • Lesson 12-2 Chords in Circles
      • Unit 7 Segment 3:Angle Properties of Inscribed and Circumscribed Circles about Triangles and Quadrilaterals >
        • Lesson 10-7 Area and Sectors in Circles
        • Lesson 12-3 InscribedAngles and Intercepted Arcs in the Circle
        • Lesson 12-4 Angles formed by Secants in the Circle
        • Lesson 12-4 Angles formed by Secants outside the Circle
      • Unit 7 Segment 4: Relationships of Sectors and their Areas >
        • Lesson 10-6 Circumference and Arclength in Circles
        • Lesson 10-7 Areas of Circles and Sectors
    • Unit 8 Surface Area and Volume >
      • Unit 8 Segment 1: Derivation of Area and Volume Formulas
      • Unit 8 Segment 2: Applications of Volume Formulas
      • Unit 8 Segment 3: Cross Sections and Transformations
    • Unit 9 Probability >
      • Unit 9 Segment 1: Independent and Conditional Probability
      • Unit 9 Segment 2: Computing Probability of Compound Events
      • Unit 9 Segment 3: Applications of Probability
  • Geometry Blog
  • Algebra 2 Blog
  • Parent Resources
  • Algebra 1
    • Unit 1 Relationships Between Quantities and Reasoning with Equations >
      • Unit 1 Segment 1: Parts of Equations
      • Unit 1 Segment 2: Solving and Modeling Equations, Justify >
        • Solving Multi-Step Equantions and Inequalities
      • Unit 1 Segment 3: Solving and Model Inequalities
      • Unit 1 Segment 4: Graph Equations and Inequalities >
        • Modeling Word Problems
    • Unit 2 Linear and Exponential Relationships >
      • Unit 2 Segment 1: Properties of Functions >
        • Function, Tables, and Graphs
        • Transformations
        • Linear Equations and Graphing
      • Unit 2 Segment 2: Systems >
        • Solving Systems of Equations
    • Unit 3 Descriptive Statistics >
      • Unit 3 Segment 1: Box Plots
      • Unit 3 Segment 2: Scatter Plots
    • Unit 4: Expressions and Equations >
      • Unit 4 Segment 1: Polynomials >
        • Properties of Exponents and Radicals
        • Polynomials
    • Unit 4 Segment 2: Quadratic Operations
    • UNIT 5 Quadratic Functions and Modeling >
      • Unit 5 Segment 1: Quadratic Functions >
        • Graphing Quadratic Equations
        • Solving Quadratic Equations
      • Unit 5 Segment 2: Modeling Functions >
        • Rational Expressions
  • Extra Credit
  • Algebra 1 Blog
  • CAHSEE PREP
Unit Overview:

This unit focuses on the relationships of transformations and the properties of parallel lines.  These two subjects are linked together because vertical angles, corresponding angles, alternate interior angles, …etc. can be described using transformations.  These properties are, then, used to prove theorems about lines and angles.  The combination of these topics use deductive reasoning from the properties of parallel lines will lead the proof of the Triangle Angle Sum Theorem.  In order for this unit to be successful, students need to have the main definitions of basic geometry terms.  After this unit, students will be able to prove congruencies of geometric figures using the foundation of this unit.

Enduring Understanding:  

  • Objects in space can be oriented in an infinite number of ways to prove congruence.
  • Properties of parallel lines cut by a transversal are preserved through different transformations.


Essential Questions:

  • How can you use the concept of transformations to prove the relationship of angle pairs of parallel lines cut by a transversal?
  • How can you apply parallel lines cut by a transversal to prove the Triangle Angle Sum Theorem?

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