Honors Geometry

Tim Brzezinski, Stephanie Kong, 2020/09/02

目次

  1. Introduction
    1. Growing from a point
    2. Geometric Objects and Definitions
    3. Applying Vocabulary Terms
    4. Line Constructions
  2. Unit 1
    1. Messing With Lisa
    2. Congruent Segments: Quick Exploration
    3. Animation 18
    4. Congruent Angles: Definition
    5. Animation 36
    6. Midpoint Definition
    7. Segment Bisectors (Definitions)
    8. Perpendicular Bisector Definition
    9. Angle Bisector Definition
    10. Parallel & Perpendicular Consequence
    11. Complementary Angles Meaning
    12. Supplementary Angles Meaning
    13. Vertical Angles Theorem
    14. Animation 1
    15. Vertical Angles Exploration (2)
  3. Unit 1a: Parallel & Perpendicular Lines in Coordinate Plane
    1. Slope Illustrator
    2. Parallel Consequence? (VA)
    3. Parallel & Perpendicular Consequence
    4. Slope Triangle Rotation (VA)
    5. Perpendicular Lines Investigation (VB)
  4. Unit 2
    1. Proving Segments Congruent (Exercise)
    2. Proving Angles Congruent (1)
    3. Proving Angles Congruent (2)
    4. Proving Angles Congruent
    5. Proof Prompt (A)
    6. Proof Prompt (B)
    7. Proof Prompt (C)
    8. Proof Prompt (D)
  5. Unit 3
    1. Transversal Intersects Parallel Lines
    2. Corresponding Angles: Quick Investigation
    3. Congruent Corresponding Angles to Start? (Quick Investigation)
    4. Corresponding Angles and Parallel Lines
    5. Alternate Interior Angles: Quick Investigation
    6. Alternate Interior Angles and Parallel Lines
    7. Exploring Alternate Interior Angles (V2)
    8. Alternate Exterior Angles: Quick Investigation
    9. Alternate Exterior Angles and Parallel Lines
    10. Exploring Alternate Exterior Angles (V2)
    11. Same-Side-Interior Angles: Quick Investigation
    12. Same Side Interior Angles and Parallel Lines
    13. Same-Side-Exterior Angles: Quick Investigation
    14. Same Side Exterior Angles and Parallel Lines
  6. Polygon Interior & Exterior Angle Sum Theorems
    1. Convex vs. Concave
    2. Triangle Angle Theorems
    3. Triangle Angle Theorems (V2)
    4. Quadrilateral Angle Theorems
    5. Pentagon Angle Theorems
    6. Hexagon Angle Theorems
    7. Heptagon Angle Theorems
    8. Octagon Angle Theorems
    9. Triangle Exterior Angle
    10. Obvious Corollary
    11. Acute Angles of a Right Triangle
  7. Congruent Triangles
    1. Proving Tri's Congruent (I)
    2. Proving Tri's Congruent (II)
    3. SAS - Exercise 1A
    4. SAS - Exercise 1B
    5. SAS - Exercise 2
    6. SAS - Exercise 3
    7. SAS: Dynamic Proof!
    8. SSS: Dynamic Proof!
    9. SSS: Dynamically Illustrated
    10. ASA Theorem?
    11. SSA Theorem?
    12. Isosceles Triangle Theorem: Discovery Lab
    13. A Special Triangle & Its Properties (I)
    14. Converse of IST (V1)
    15. Another Special Triangle and its Properties (II)
    16. Converse of IST: Template
    17. Converse of IST (II)
    18. HL: Hypotenuse-Leg Action!
  8. Coordinate Geometry Accessories
    1. Slope to Angle Measure Calculator (I)
  9. Some Locus Theorems
    1. Interesting Coplanar Locations (1)
    2. Interesting Coplanar Locations (2)
    3. Another Special Theorem: Part 1 (V1)
    4. Another Special Theorem: Part 2 (V1)
    5. Animation 57
    6. Animation 58
  10. Constructions (Compass & Straightedge)!
    1. Congruent Segments Construction (I)
    2. Congruent Angle: Construction
    3. Angle Bisector: Construction
    4. Perpendicular Line: Construction 1
    5. Perpendicular Line: Construction 2
    6. Perpendicular Bisector: Construction
    7. Parallel Line: Constructions
    8. Congruent Triangle: Construction
    9. Other Constructions: 1
    10. Other Constructions: 2
    11. Regular Hexagon Construction Template
    12. Equilateral Triangle Construction Template
    13. Square Construction Template
  11. Points of Concurrency
    1. Points of Concurrency: Investigation
    2. Orthocenter Exploration
    3. Circumcenter (& Questions)
    4. Circumcenter & Circumcircle Action!
    5. Circumcircle: Construction Exercise (VA)
    6. Incenter Exploration (A)
    7. Incenter Exploration (B)
    8. Incenter & Incircle Action!
    9. Incenter + Incircle Action (V2)!
    10. Incircle: Construction Exercise (VA)
    11. Medians and Centroid Dance
    12. Animation 25
    13. Medians & Equal Areas!
  12. Parallelograms & Other Triangle Theorems
    1. Parallelogram Construction Template & Discovery Lab
    2. Parallelogram: Theorem 1
    3. Parallelogram: Theorem 2
    4. Parallelogram: Theorem (3)
    5. What Kind of Quadrilateral is This? (Part 1)
    6. What Kind of Quadrilateral is This? (Part 2)
    7. What Kind of Quadrilateral is This? (Part 3)
    8. What Kind of Quadrilateral is This? (Part 4)
    9. Special Quadrilateral: Theorem 1
    10. Special Quadrilateral: Theorem 2
    11. Special Quadrilateral: Theorem 3
    12. Special Quadrilateral: Theorem 4
    13. Effortless Trisections
    14. Special Line through Triangle V2 (Theorem Discovery)
    15. Triangle Midsegment Action!
  13. Special Quadrilaterals: Investigations
    1. Rhombus Template with Investigation Questions
    2. Rectangle Template with Investigation Questions
    3. Square Template with Investigation Questions
    4. Trapezoids: Median Investiagtion
    5. Isosceles Trapezoid Template
    6. Kite Template with Investigation Questions
  14. Special Quadrilaterals: Illustrations without Words
    1. Rhombus Action!
    2. Rectangle Action!
    3. Square Action!
    4. Trapezoid Median (Midsegment) Action!
    5. Isosceles Trapezoid Action!
    6. Kite Action!
  15. Special Quadrilaterals: Quick Reference Applets
    1. Rhombus Template (Scaffolded Discovery)
    2. Scaffolded Rectangle Template
    3. Square Template (Scaffolded Investigation)
    4. Isosceles Trapezoid Template (Scaffolded Discovery)
    5. Kite Template: Scaffolded Investigation
  16. Coordinate Geometry Proof Prompts
    1. Parallelogram: Coordinate Geometry Setup
    2. Parallelogram Diagonals
    3. Isosceles Triangle Medians
    4. Rectangle Diagonals
    5. Isosceles Trapezoid Diagonals
    6. Isosceles Trapezoid Midpoints
    7. Rhombus Diagonals
    8. Inscribed Angle Intercepts Semicircle
    9. 3 Special Points!
    10. Finsler-Hadwiger Action!!!
    11. Finsler-Hadwiger Exercise (VA)
    12. Finsler-Hadwiger Exercise (VB)
    13. Triangle Inequality: Discovery Lesson
  17. Triangle Inequality
    1. Triangle Inequality: Discovery Lesson
    2. Triangle Side Possibilities? (V2)
    3. Triangle Inequality
    4. Triangle Inequality (II)
    5. Inequalities in 1 Triangle
  18. Dilations: Discovery Activities & Exercises
    1. Dilating a Point (Intro)
    2. Dilating a Line: HSG.SRT.A.1.A
    3. Dilating a Segment: HSG.SRT.A.1.B
    4. Properties of Dilations
    5. Properties of Dilations (II)
  19. Similarity!
    1. Proving Triangles Similar (1)
    2. Proving Triangles Similar (2)
    3. Proving Triangles Similar (3)
    4. Proving Triangles Similar (4)
    5. Angle -Angle: Triangle Investigation
    6. AA Similarity Theorem
    7. SAS ~ Theorem
    8. SSS ~ Theorem (V1)
    9. SSSS: Similar Quads?
    10. AAA: Similar Quads?
    11. Parallel Lines Proportionality Theorem
    12. Parallel Lines Proportionality Theorem
    13. Triangle-Angle Bisector Theorem
    14. Similar Circles?
  20. Similarity in RIGHT TRIANGLES
    1. Similar Right Triangles (V1)
    2. Acute, Right, Obtuse (III)
    3. Acute, Right, or Obtuse?
    4. Special Right Triangle (I)
    5. Another Special Right Triangle (Guided Discovery)
    6. Special Right Triangle (II)
    7. Right Triangle Trigonometry: Intro
    8. Trigonometric Ratios (Right Triangle Context)
    9. What "CO" in COsine Means
    10. How Fast are You Spinning?
  21. Circles
    1. Circle Terminology
    2. Circle vs. Sphere
    3. Circle Tangent-Types Illustrator
    4. Tangents to Circles: Investigation
    5. Properties of Tangents Drawn to Circles (A)
    6. Congruent Chords: Quick Investigation
    7. Congruent Chords (I)
    8. Diameters & Chords I (VA)
    9. Diameters & Chords I (VB)
    10. Congruent Chords Action (A)
    11. Equidistant Chord Action
    12. Where to Sit? (I)
    13. Where to Sit (II)?
    14. Inscribed Angle Theorem: Take 2!
    15. Inscribed Angle Theorem (V1)
    16. Inscribed Angle Theorem: Corollary 1
    17. Animation 20 (Inscribed Angle Dance!)
    18. Thales' Theorem (VA)
    19. Cyclic Quadrilaterals (IAT: Corollary 3)
    20. Circumcircle: Construction Exercise (VA)
    21. Where in NYC? (VA)
    22. Incircle: Construction Exercise (VA)
    23. Angle Formed by Chord & Tangent (I)
    24. Angle Formed by Chord & Tangent (II)
    25. Angle Formed by 2 Chords (I)
    26. Angle Formed by 2 Chords (II)
    27. Angles from Secants and Tangents (V1)
    28. Angle From 2 Secants (V2)
    29. Crossing Chords: Proof Hint
    30. Crossing Chords Property & Proof Start (II)
    31. Crossing Chords Property & Proof Start
    32. Secants: Proof Hint

1.

Introduction

  • 1. Growing from a point
  • 2. Geometric Objects and Definitions
  • 3. Applying Vocabulary Terms
  • 4. Line Constructions

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2.

Unit 1

  • 1. Messing With Lisa
  • 2. Congruent Segments: Quick Exploration
  • 3. Animation 18
  • 4. Congruent Angles: Definition
  • 5. Animation 36
  • 6. Midpoint Definition
  • 7. Segment Bisectors (Definitions)
  • 8. Perpendicular Bisector Definition
  • 9. Angle Bisector Definition
  • 10. Parallel & Perpendicular Consequence
  • 11. Complementary Angles Meaning
  • 12. Supplementary Angles Meaning
  • 13. Vertical Angles Theorem
  • 14. Animation 1
  • 15. Vertical Angles Exploration (2)

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Unit 1a: Parallel & Perpendicular Lines in Coordinate Plane

  • 1. Slope Illustrator
  • 2. Parallel Consequence? (VA)
  • 3. Parallel & Perpendicular Consequence
  • 4. Slope Triangle Rotation (VA)
  • 5. Perpendicular Lines Investigation (VB)

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Unit 2

  • 1. Proving Segments Congruent (Exercise)
  • 2. Proving Angles Congruent (1)
  • 3. Proving Angles Congruent (2)
  • 4. Proving Angles Congruent
  • 5. Proof Prompt (A)
  • 6. Proof Prompt (B)
  • 7. Proof Prompt (C)
  • 8. Proof Prompt (D)

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Unit 3

  • 1. Transversal Intersects Parallel Lines
  • 2. Corresponding Angles: Quick Investigation
  • 3. Congruent Corresponding Angles to Start? (Quick Investigation)
  • 4. Corresponding Angles and Parallel Lines
  • 5. Alternate Interior Angles: Quick Investigation
  • 6. Alternate Interior Angles and Parallel Lines
  • 7. Exploring Alternate Interior Angles (V2)
  • 8. Alternate Exterior Angles: Quick Investigation
  • 9. Alternate Exterior Angles and Parallel Lines
  • 10. Exploring Alternate Exterior Angles (V2)
  • 11. Same-Side-Interior Angles: Quick Investigation
  • 12. Same Side Interior Angles and Parallel Lines
  • 13. Same-Side-Exterior Angles: Quick Investigation
  • 14. Same Side Exterior Angles and Parallel Lines

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6.

Polygon Interior & Exterior Angle Sum Theorems

  • 1. Convex vs. Concave
  • 2. Triangle Angle Theorems
  • 3. Triangle Angle Theorems (V2)
  • 4. Quadrilateral Angle Theorems
  • 5. Pentagon Angle Theorems
  • 6. Hexagon Angle Theorems
  • 7. Heptagon Angle Theorems
  • 8. Octagon Angle Theorems
  • 9. Triangle Exterior Angle
  • 10. Obvious Corollary
  • 11. Acute Angles of a Right Triangle

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7.

Congruent Triangles

  • 1. Proving Tri's Congruent (I)
  • 2. Proving Tri's Congruent (II)
  • 3. SAS - Exercise 1A
  • 4. SAS - Exercise 1B
  • 5. SAS - Exercise 2
  • 6. SAS - Exercise 3
  • 7. SAS: Dynamic Proof!
  • 8. SSS: Dynamic Proof!
  • 9. SSS: Dynamically Illustrated
  • 10. ASA Theorem?
  • 11. SSA Theorem?
  • 12. Isosceles Triangle Theorem: Discovery Lab
  • 13. A Special Triangle & Its Properties (I)
  • 14. Converse of IST (V1)
  • 15. Another Special Triangle and its Properties (II)
  • 16. Converse of IST: Template
  • 17. Converse of IST (II)
  • 18. HL: Hypotenuse-Leg Action!

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8.

Coordinate Geometry Accessories

  • 1. Slope to Angle Measure Calculator (I)

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Some Locus Theorems

  • 1. Interesting Coplanar Locations (1)
  • 2. Interesting Coplanar Locations (2)
  • 3. Another Special Theorem: Part 1 (V1)
  • 4. Another Special Theorem: Part 2 (V1)
  • 5. Animation 57
  • 6. Animation 58

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Constructions (Compass & Straightedge)!

Contains various compass and straightedge geometry construction exercises

  • 1. Congruent Segments Construction (I)
  • 2. Congruent Angle: Construction
  • 3. Angle Bisector: Construction
  • 4. Perpendicular Line: Construction 1
  • 5. Perpendicular Line: Construction 2
  • 6. Perpendicular Bisector: Construction
  • 7. Parallel Line: Constructions
  • 8. Congruent Triangle: Construction
  • 9. Other Constructions: 1
  • 10. Other Constructions: 2
  • 11. Regular Hexagon Construction Template
  • 12. Equilateral Triangle Construction Template
  • 13. Square Construction Template

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Points of Concurrency

  • 1. Points of Concurrency: Investigation
  • 2. Orthocenter Exploration
  • 3. Circumcenter (& Questions)
  • 4. Circumcenter & Circumcircle Action!
  • 5. Circumcircle: Construction Exercise (VA)
  • 6. Incenter Exploration (A)
  • 7. Incenter Exploration (B)
  • 8. Incenter & Incircle Action!
  • 9. Incenter + Incircle Action (V2)!
  • 10. Incircle: Construction Exercise (VA)
  • 11. Medians and Centroid Dance
  • 12. Animation 25
  • 13. Medians & Equal Areas!

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Parallelograms & Other Triangle Theorems

  • 1. Parallelogram Construction Template & Discovery Lab
  • 2. Parallelogram: Theorem 1
  • 3. Parallelogram: Theorem 2
  • 4. Parallelogram: Theorem (3)
  • 5. What Kind of Quadrilateral is This? (Part 1)
  • 6. What Kind of Quadrilateral is This? (Part 2)
  • 7. What Kind of Quadrilateral is This? (Part 3)
  • 8. What Kind of Quadrilateral is This? (Part 4)
  • 9. Special Quadrilateral: Theorem 1
  • 10. Special Quadrilateral: Theorem 2
  • 11. Special Quadrilateral: Theorem 3
  • 12. Special Quadrilateral: Theorem 4
  • 13. Effortless Trisections
  • 14. Special Line through Triangle V2 (Theorem Discovery)
  • 15. Triangle Midsegment Action!

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Special Quadrilaterals: Investigations

  • 1. Rhombus Template with Investigation Questions
  • 2. Rectangle Template with Investigation Questions
  • 3. Square Template with Investigation Questions
  • 4. Trapezoids: Median Investiagtion
  • 5. Isosceles Trapezoid Template
  • 6. Kite Template with Investigation Questions

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Special Quadrilaterals: Illustrations without Words

  • 1. Rhombus Action!
  • 2. Rectangle Action!
  • 3. Square Action!
  • 4. Trapezoid Median (Midsegment) Action!
  • 5. Isosceles Trapezoid Action!
  • 6. Kite Action!

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Special Quadrilaterals: Quick Reference Applets

  • 1. Rhombus Template (Scaffolded Discovery)
  • 2. Scaffolded Rectangle Template
  • 3. Square Template (Scaffolded Investigation)
  • 4. Isosceles Trapezoid Template (Scaffolded Discovery)
  • 5. Kite Template: Scaffolded Investigation

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Coordinate Geometry Proof Prompts

Contains applets that serve as prompts and dynamic informal illustrations of geometric proofs that can be proven using coordinate geometry and/or congruent triangles.

  • 1. Parallelogram: Coordinate Geometry Setup
  • 2. Parallelogram Diagonals
  • 3. Isosceles Triangle Medians
  • 4. Rectangle Diagonals
  • 5. Isosceles Trapezoid Diagonals
  • 6. Isosceles Trapezoid Midpoints
  • 7. Rhombus Diagonals
  • 8. Inscribed Angle Intercepts Semicircle
  • 9. 3 Special Points!
  • 10. Finsler-Hadwiger Action!!!
  • 11. Finsler-Hadwiger Exercise (VA)
  • 12. Finsler-Hadwiger Exercise (VB)
  • 13. Triangle Inequality: Discovery Lesson

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Triangle Inequality

  • 1. Triangle Inequality: Discovery Lesson
  • 2. Triangle Side Possibilities? (V2)
  • 3. Triangle Inequality
  • 4. Triangle Inequality (II)
  • 5. Inequalities in 1 Triangle

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Dilations: Discovery Activities & Exercises

  • 1. Dilating a Point (Intro)
  • 2. Dilating a Line: HSG.SRT.A.1.A
  • 3. Dilating a Segment: HSG.SRT.A.1.B
  • 4. Properties of Dilations
  • 5. Properties of Dilations (II)

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Similarity!

Contains similarity applets.

  • 1. Proving Triangles Similar (1)
  • 2. Proving Triangles Similar (2)
  • 3. Proving Triangles Similar (3)
  • 4. Proving Triangles Similar (4)
  • 5. Angle -Angle: Triangle Investigation
  • 6. AA Similarity Theorem
  • 7. SAS ~ Theorem
  • 8. SSS ~ Theorem (V1)
  • 9. SSSS: Similar Quads?
  • 10. AAA: Similar Quads?
  • 11. Parallel Lines Proportionality Theorem
  • 12. Parallel Lines Proportionality Theorem
  • 13. Triangle-Angle Bisector Theorem
  • 14. Similar Circles?

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Similarity in RIGHT TRIANGLES

  • 1. Similar Right Triangles (V1)
  • 2. Acute, Right, Obtuse (III)
  • 3. Acute, Right, or Obtuse?
  • 4. Special Right Triangle (I)
  • 5. Another Special Right Triangle (Guided Discovery)
  • 6. Special Right Triangle (II)
  • 7. Right Triangle Trigonometry: Intro
  • 8. Trigonometric Ratios (Right Triangle Context)
  • 9. What "CO" in COsine Means
  • 10. How Fast are You Spinning?

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Circles

  • 1. Circle Terminology
  • 2. Circle vs. Sphere
  • 3. Circle Tangent-Types Illustrator
  • 4. Tangents to Circles: Investigation
  • 5. Properties of Tangents Drawn to Circles (A)
  • 6. Congruent Chords: Quick Investigation
  • 7. Congruent Chords (I)
  • 8. Diameters & Chords I (VA)
  • 9. Diameters & Chords I (VB)
  • 10. Congruent Chords Action (A)
  • 11. Equidistant Chord Action
  • 12. Where to Sit? (I)
  • 13. Where to Sit (II)?
  • 14. Inscribed Angle Theorem: Take 2!
  • 15. Inscribed Angle Theorem (V1)
  • 16. Inscribed Angle Theorem: Corollary 1
  • 17. Animation 20 (Inscribed Angle Dance!)
  • 18. Thales' Theorem (VA)
  • 19. Cyclic Quadrilaterals (IAT: Corollary 3)
  • 20. Circumcircle: Construction Exercise (VA)
  • 21. Where in NYC? (VA)
  • 22. Incircle: Construction Exercise (VA)
  • 23. Angle Formed by Chord & Tangent (I)
  • 24. Angle Formed by Chord & Tangent (II)
  • 25. Angle Formed by 2 Chords (I)
  • 26. Angle Formed by 2 Chords (II)
  • 27. Angles from Secants and Tangents (V1)
  • 28. Angle From 2 Secants (V2)
  • 29. Crossing Chords: Proof Hint
  • 30. Crossing Chords Property & Proof Start (II)
  • 31. Crossing Chords Property & Proof Start
  • 32. Secants: Proof Hint

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21.21.

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21.22.

–

21.23.

–

21.24.

–

21.25.

–

21.26.

–

21.27.

–

21.28.

–

21.29.

–

21.30.

–

21.31.

–

21.32.

–

情報