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CCSS High School: Geometry

Anthony DiLaura, Aug 15, 2016

This GeoGebra Book contains hundreds of discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of geometry concepts both inside and outside of the mathematics classroom. his GeoGebra Book also contains contributions from the following individuals and organizations: Anthony C.M. OR Steve Phelps Jennifer Silverman Dr. Ted Coe sonom Samantha Cruz Terry Lee Lindenmuth Raúl Manuel Falcón Ganfornina Walch Education EDC in Maine Without their amazing talent and creativity, this resource would not have been possible.

1.

Welcome! (Introduction)

1. Geometry Resources

1.1.

2.

HSG.CO.A.1

1. Congruent Segments: Quick Exploration
2. Animation 18
3. Congruent Angles: Definition
4. Animation 36
5. Midpoint Definition
6. Animation 56
7. Segment Bisectors (Definitions)
8. Perpendicular Bisector Definition
9. Animation 15
10. Angle Bisector Definition (I)
11. Complementary Meaning?
12. Animation 48
13. Supplementary Angles (Quick Exploration)
14. Animation 19
15. Circle vs. Sphere

HSG.CO.A.2, A.3, A.4, A.5

1. Translations and Rotations
2. Translating Triangle by a Vector
3. Reflections
4. Reflections Introduction
5. Flip Flop Reflection
6. Tool for compositions of rigid transformations and dilations
7. Applet for Multiple Transformations
8. Messing With Lisa
9. Rotations: Introduction
10. Reflections and Translations
11. Tessellation by Translation
12. Parallel Translation
13. Transformations: Exercise 1
14. Transformations: Exercise 2
15. Transformations: Exercise 3

HSG.CO.B.6

1. Are the triangles congruent (part 2)?
2. Are the triangles congruent (part 3)?

HSG.CO.C.9

1. Vertical Angles Theorem
2. Animation 1
3. Exploring Corresponding Angles (V2)
4. Alternate Interior Angles Theorem (V1)
5. Exploring Alternate Interior Angles (V2)
6. Alternate Interior Angles Theorem (V3)
7. Animation 16
8. Alternate Exterior Angles Theorem (V1)
9. Exploring Alternate Exterior Angles (V2)
10. Animation 39
11. Animation 60
12. Same Side Interior Angles Theorem
13. Animation 29
14. Exploring Same Side Exterior Angles
15. Animation 73
16. Solution to Parallel Lines & Angles Problem
17. A Special Theorem: Part 1 (V1)
18. A Special Theorem: Part 2 (V1)
19. Animation 57
20. Another Special Theorem: Part 1 (V1)
21. Another Special Theorem: Part 2 (V1)
22. Animation 58

HSG.CO.C.10

1. Area of a Triangle (Discovery)
2. Triangle Angle Theorems
3. Triangle Angle Theorems (V2)
4. Transformation Proof 3
5. Triangle Angle Sum Theorem
6. Animation 2
7. Triangle Exterior Angle
8. Exterior Angles of a Triangle
9. Animation 22
10. Isosceles Triangle Theorem: Discovery Lab
11. A Special Triangle & Its Properties (I)
12. Animation 8
13. Converse of IST (V1)
14. Animation 82
15. Animation 23
16. Another Special Triangle and its Properties (II)
17. Animation 27
18. Converse of IST (II)
19. Animation 84
20. Special Right Triangle (I)
21. Animation 59
22. Special Right Triangle (II)
23. Another Special Right Triangle (Guided Discovery)
24. Animation 42
25. Triangle Midsegment Action!
26. Midsegment of a Triangle
27. Points of Concurrency: Investigation
28. Orthocenter Exploration
29. Circumcenter (& Questions)
30. Circumcenter & Circumcircle Action!
31. Animation 28
32. Midpoint of HYP
33. Animation 46
34. Incenter Exploration (A)
35. Incenter Exploration (B)
36. Incenter & Incircle Action!
37. Animation 17
38. Medians Centroid Theorem (Proof without Words)
39. Medians and Centroid Dance
40. Animation 25
41. Medians & Equal Areas!
42. Animation 74
43. Animation 90
44. Euler Line (Informal Investigation)
45. Napoleon Motion!
46. Animation 14
47. Vivani Action!
48. Equilateral Action (1)!
49. Animation 91
50. Equilateral Action (2)!
51. Animation 94
52. Equilateral Action (3)!
53. 9 Point Circle Action
54. 9-Point Circle Action (Part 2)
55. 9-Point Circle Action (Part 3A)
56. 9-Point Circle Action (Part 3B)
57. 9-Point Circle Action (Part 4)
58. 9-Point Circle (Informal Investigation)
59. Euler Line Generator

HSG.CO.C.11

1. Parallelogram: Area
2. Parallelogram Construction Template & Discovery Lab
3. Parallelogram Template (Scaffolded Discovery)
4. Parallelogram Template
5. Parallelograms (I)
6. Animation 75
7. Animation 80
8. Animation 6
9. What Kind of Quadrilateral is This? (Part 1)
10. Congruent Opposite Sides of a Quadrilateral
11. Quadrilateral With Opposite Angles Congruent
12. What Kind of Quad?
13. Quadrilateral Investigation (I)
14. Rhombus Action!
15. Animation 11
16. Rhombus Template (Scaffolded Investigation)
17. Rhombus Template
18. Rectangle Action!
19. Animation 31
20. Rectangle Template (Scaffolded Investigation)
21. Rectangle Template with Investigation Questions
22. Square Action!
23. Animation 41
24. Trapezoids: Median Investiagtion
25. Trapezoid Median (Midsegment) Action!
26. Animation 67
27. Trapezoid Median: 2 Discoveries
28. Isosceles Trapezoid Action!
29. Animation 64
30. Animation 35
31. Isosceles Trapezoid Template (Scaffolded Investigation)
32. Isosceles Trapezoid Template
33. Animation 49
34. Kite Action!
35. Animation 26
36. Kite Template (Scaffolded Investigation)
37. Quad Midpoints Action!
38. Thebault Action!!!
39. Animation 83

HSG.CO.D.12

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. Centroid Construction Challenge #1
12. Possible Solution for Centroid Challenge #1
13. Centroid Construction Challenge #2
14. Possible Solution for Centroid Construction Challenge #2
15. Centroid Construction Challenge #3
16. Possible solution to Centroid Construction Challenge #3
17. Triangle Construction Challenge #1
18. Possible solution to Triangle Construction Challenge #1
19. Triangle Consruction Challenge #2
20. Possible solution to Triangle Construction Challenge #2
21. Triangle Construction Challenge #3
22. Potential solution for Triangle Construction Challenge #3
23. Bizzare Trisection?

HSG.CO.D.13

1. Equilateral Triangle Construction Template
2. Square Construction Template
3. Regular Hexagon Construction Template

HSG.SRT.A.1, A.1.A, A.1.B

1. Dilation Introduction: Transformers!
2. Dilating a Point (Intro)
3. Dilating a Line: HSG.SRT.A.1.A
4. Dilating a Segment: HSG.SRT.A.1.B

HSG.SRT.A.2

1. Properties of Dilations
2. Properties of Dilations (II)

HSG.SRT.A.3

1. AA Similarity Theorem
2. Animation 97
3. AAA: Similar Quads?

HSG.SRT.B.4 & B.5

1. SAS ~ Theorem
2. SSS ~ Theorem (V1)
3. Animation 63
4. SSS ~ Theorem (V2)
5. SSSS: Similar Quads?
6. Similar Right Triangles (V1)
7. Animation 13
8. Pythagorean and similar triangles.
9. Parallel Lines Proportionality Theorem
10. Triangle-Angle Bisector Theorem
11. Animation 81
12. Proof Without Words
13. Proof Without Words
14. Proof Without Words
15. Proof Without Words
16. Proof Without Words
17. Proof Without Words
18. Proof Without Words
19. Proof Without Words
20. Proof Without Words
21. Proof Without Words
22. Wordless Pythagorean Theorem based on Translations

HSG.SRT.C.6 & C.7 & C.8

1. Right Triangle Trigonometry: Intro
2. Discovering Sine, Cosine, and Tangent in Right Triangles
3. Trigonometric Ratios (Right Triangle Context)
4. What "CO" in COsine Means
5. Animation 98
6. Animation 99
7. Animation 100
8. How Fast are You Spinning?

HSG.SRT.D.9 & D.10 & D.11

1. Law of Sines (& Area)
2. Law of Sines (Illustrated)
3. Law of Cosines: Discovery
4. law of cosines (proof)

HSG.C.A.1

1. Congruent Circles: Definition
2. Animation 89
3. Similar Circles?

HSG.C.A.2

1. Circle Terminology
2. Properties of Tangents Drawn to Circles (A)
3. Properties of Tangents Drawn to Circles (B)
4. Animation 3
5. Where to Sit? (I)
6. Where to Sit (II)?
7. Inscribed Angle Theorem (V1)
8. Animation 12
9. Inscribed Angle Theorem: Corollary 1
10. Animation 20 (Inscribed Angle Dance!)
11. Thales' Theorem (VB)
12. Animation 54
13. Angle Formed by Chord & Tangent (I)
14. Animation 50
15. Angle Formed by Chord & Tangent (II)
16. Animation 78
17. Congruent Chords (I)
18. Animation 76
19. Diameters & Chords I (VA)
20. Diameters & Chords I (VB)
21. Animation 24
22. Congruent Chords Action (A)
23. Animation 96
24. Equidistant Chord Action
25. Animation 101
26. Angle Formed by 2 Chords (I)
27. Animation 32
28. Angle Formed by 2 Chords (II)
29. Animation 33
30. Angles from Secants and Tangents (V1)
31. Animation 61
32. Angle From 2 Secants (V2)
33. Animation 45
34. Crossing Chords: Proof Hint
35. Animation 79
36. Crossing Chords Property & Proof Start
37. Crossing Chords Property & Proof Start (II)
38. Secants: Proof Hint
39. Animation 88
40. Animation 92
41. Tangents to Circles: Investigation

HSG.C.A.3

1. Circumcircle: Construction Exercise (VA)
2. Circumcircle: Construction Exercise (VB)
3. Incircle: Construction Exercise (VA)
4. Incircle: Construction Exercise (VB)
5. Cyclic Quadrilaterals (IAT: Corollary 3)
6. Animation 43

HSG.C.A.4

1. Tangent to Circle: Construction 1
2. Tangent to Circle: Construction 2

HSG.C.B.5

1. Radius Unwrapper v2.0
2. 1 Radian: Clear Definition
3. Movie: Radians to Revs
4. Arc length: Quick Investigation
5. Area of a Sector

HSG.GPE.A.1

1. Circle Equation: Center (0,0)
2. Circle Equation: Center NOT (0,0)
3. Circle Equation: Center (h,k)
4. Equation & Graph of a Circle

HSG.GPE.B.4

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. Slope to Angle Measure Calculator (I)
11. Slope to Angle Measure Calculator (II)

HSG.GPE.B.5

1. Parallel & Perpendicular Consequence
2. Slope Triangle Rotation (VA)
3. Parallel Lines Definition
4. Perpendicular Lines Definition (& Consequence)

HSG.GPE.B.6

1. Endpoint (x,y) of a Segment Given Midpoint & Other Endpoint
2. Midpoint (x,y) of a Segment in the Coordinate Plane (Quiz)
3. Partition Line Segments

HSG.GPE.B.7

1. Distance in the Coordinate Plane (With Hints)
2. Distance in the Coordinate Plane (II)
3. Distance in the Coordinate Plane (Quiz without Grid)
4. Distance in the Coordinate Plane (Quiz With Grid)

HSG.GMD.A.1

1. TRUE MEANING of π
2. Circumference = ? (Animation)
3. Animation 66
4. Circumference = ? (Animation II)
5. Animation 70
6. Animation 65
7. Circle Area (by Peeling)
8. Circle Area (By Peeling!)
9. Area of a Circle (III)
10. Area of a Circle (by Peeling)
11. Area of a Circle II
12. Area of a Circle - without words (Animation 38)
13. Figure 6.7 Cavalieri's principle
14. Cavalieri's Principle
15. Volume of a Rectangular Prism
16. Trisecting the Cube into 3 Pyramids
17. Volume of Pyramids
18. Volume of Pyramids - Chinese Proof

HSG.GMD.A.2 & A.3

1. Volume of Spheres
2. Volume of Spheres with Proof
3. A sphere in a cylinder.
4. Surface Area of Spheres
5. Volumes and Surface Areas of Similar Cuboids
6. oblique and right pyramid - Cavalieri
7. Right Triangular Prism!
8. Adjustable Triangular Prism
9. Right Circular Cylinder!
10. Sphere Peeling: Volume
11. Net of a Cone
12. Curved Surface Area of Cones (Combined Version)

HSG.GMD.B.4

1. Sections of Rectangular Prisms (Cuboids)
2. Sections of Triangular Prisms
3. Sections of Cylinders
4. Sections of Rectangular Pyramids
5. Sections of Triangular Pyramids
6. Sections of Cones
7. Sections of Spheres
8. Exploring Sections of Cubes
9. 11 Nets of the Cube
10. Cube Geometry: Shortest Path Between Points - A Net
11. Cube Dissection Problem
12. Rotating a Triangle Around a Coordinate Axis
13. Cross Section? (1)

HSG.MG.A.1 & A.2 & A.3

1. Panteón (Roma)
2. Golden Gate (San Francisco)
3. Plaza de toros (Ronda)
4. Big Ben (Londres)
5. Museo Guggenheim (New York)
6. Edificio CEOE (Zaragoza)
7. Homer^3
8. Taj Mahal (Agra)
9. 4-Stroke Engine
10. CCGPS AG 3.5.3 Example 3
11. Optimization - Box
12. Volume of a 3-sided Rectangular Solid (Prism)

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CCSS High School: Geometry

Table of Contents

Welcome! (Introduction)

HSG.CO.A.1

HSG.CO.A.2, A.3, A.4, A.5

HSG.CO.B.6

HSG.CO.B.7

HSG.CO.B.8

HSG.CO.C.9