Triangle Inequality and Angle Sum: Solving and Detecting Impossible Triangles

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1Rewrite Expressions With Distribution and Like Terms (and Check by Substitution)2Translate Words Into Algebra (Variables, Units, and Meaning)3Solve One-Step and Two-Step Linear Equations (Including Fractions)4Solve Multi-Step Linear Equations With Distribution and Collecting Terms 5Equations With Variables on Both Sides (No Solution vs. Infinitely Many)6Proportions and Rates: Set Up the Equation, Track Units 7Linear Inequalities: Solve, Graph, and Use Interval Notation 8Compound Inequalities (“And” / “Or”) and Correct Solution Sets 9Error Repair: Negatives, Moving Terms, and the Inequality Sign Flip

10Points and Intercepts in Context 11Slope as Rate of Change 12Graphing Lines From Equations and From a Point Plus Slope 13Writing Linear Equations From a Graph, Two Points, and a Table 14Point-Slope Form and Converting to Slope-Intercept Form 15Function Notation, Evaluation, and Reasonable Domain and Range 16Modeling Linear Word Problems and a SAT-Style Mixed Checkpoint

17Systems From Word Problems: Two Constraints, One Solution 18Solving Systems by Graphing: One, None, or Infinitely Many Solutions 19Solving Systems by Substitution (and Checking Both Equations)20Elimination and Method Choice: Multiply, Add/Subtract, Interpret Cancellations 21Exponents, Scientific Notation, and Polynomial Operations

22Factoring: GCF and Reverse Distribution 23Factoring Trinomials and Special Patterns 24Solving Quadratics by Factoring and Zeros 25Completing the Square and Vertex Form 26Solving, Graphing, Modeling, and Method Selection for Quadratics

27Simplifying Radical Expressions 28Radicals and Rational Exponents 29Solving Radical Equations and Checking for Extraneous Solutions 30Domain Restrictions for Rational Expressions 31Simplifying Rational Expressions Legally 32Solving Rational Equations and Finishing With Mixed Algebra Practice

33Reading Geometry Diagrams: Notation, Markings, and What You Can’t Assume 34Compass-and-Straightedge Constructions You Actually Use 35Vertical Angles and Linear Pairs: The First Angle Facts You Can Justify 36Complementary and Supplementary Angles With Algebra 37Parallel Lines and a Transversal: Corresponding and Alternate Interior Angles 38Transformations on the Coordinate Plane: Translations, Reflections, Rotations, and Dilations

39Triangle Inequality and Angle Sum: Solving and Detecting Impossible Triangles

40The Exterior Angle Theorem in Triangle Angle-Chasing 41Triangle Correspondence: Matching Vertices Before You Prove Anything 42Choosing SSS, SAS, ASA, or AAS: When Is Congruence Guaranteed?43HL Congruence and the SSA Trap in Right Triangles 44Writing, Completing, and Debugging Congruence Proofs With CPCTC

45Correspondence First: Recognizing Similar Figures and Matching Parts 46Triangle Similarity Criteria: AA, SAS~, and SSS~47Solving for Unknowns With Similarity Proportions 48Indirect Measurement and the Right-Triangle Length Toolkit 49Right-Triangle Trig Ratios and a Mixed SAT-Style Checkpoint

50Angle Sums in Polygons and Key Quadrilateral Properties 51Core Circle Measures: Circumference, Area, and Pi Discipline 52Circle Theorems in Diagrams: Central vs. Inscribed Angles, Chords, and Tangents 53Area of Plane Figures and Composite Areas (Including Scale Factor Effects)54Surface Area and Volume of Solids With Unit Conversions (Mixed Review)

55Distance Formula as the Pythagorean Theorem in Disguise 56Midpoint and Segment Partition on the Coordinate Plane 57Slope Criteria for Parallel and Perpendicular Lines 58Equations of Lines for Geometric Constraints and Intersections 59Coordinate Proofs and Full Mixed Capstone Practice

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High School Algebra & Geometry
Triangle Inequality and Angle Sum: Solving and Detecting Impossible Triangles