Eureka Geometry Mod. 2 Similarity, Proof, and Trigonometry

Katie Acland, May 12, 2023

Eureka Geometry Module 2 Similarity, Proof, and Trigonometry

Table of Contents

  1. Module 2A Scale Drawings
    1. 2.04 Warm-up: Scale drawing of a segment
    2. 2.02 Make Scale Drawings with Ratio Method - Activity
    3. 2.04 Warm-up: Scale drawing of a segment - r1
    4. 2.04 Side Splitter Theorem Exploration
    5. 2.03 Scale Drawings using the Parallel Method
    6. 2.01 Scale Drawings Activity
  2. Module 2B Dilations
    1. 2.11 Warm-Up - Day 2
    2. 2.11 Warm-Up - Day 1
    3. 2.10 Activity
    4. 2.09 Warm-up
    5. 2.08 Warmup
    6. 2.07 Warm-up
    7. Dilations Part 2: What Do You Notice?
    8. Dilations of a star
  3. Module 2C Similarity and Dilations
    1. 2.17 SSS Similarity Theorem: Exploration
    2. SAS Similarity Theorem: Exploration
    3. 2.15 Warm-Up - Building Similar Triangles
    4. 2.15 Angle-Angle (AA) Similarity Theorem: Quick Investigation
    5. Lesson 2.19 - Eratosthenes and the Circumference of the Earth
    6. 2.12 Warm-Up
  4. Module 2D Applying Similarity to Right Triangles
    1. 2.21 Special Relationships within Right Triangles
    2. Similar Right Triangles (V2)
    3. Similar Right Triangles (V1)
    4. Pythagorean Theorem Proof, new in 2023
    5. Pythagorean Theorem
    6. Pythagorean Triples
    7. Converse Pythagorean Theorem
  5. Module 2E Trigonometry

1.

Module 2A Scale Drawings

  • 1. 2.04 Warm-up: Scale drawing of a segment
  • 2. 2.02 Make Scale Drawings with Ratio Method - Activity
  • 3. 2.04 Warm-up: Scale drawing of a segment - r1
  • 4. 2.04 Side Splitter Theorem Exploration
  • 5. 2.03 Scale Drawings using the Parallel Method
  • 6. 2.01 Scale Drawings Activity

1.1.

2.04 Warm-up: Scale drawing of a segment

Creating a scale drawing using the ratio method:
[list=1][*]Draw a ray [icon]/images/ggb/toolbar/mode_ray.png[/icon] beginning at the center through each vertex of the figure.[/*][*]Dilate each vertex along the appropriate ray by the scale factor. For example for a scale factor r = 1/2, find the midpoint [icon]/images/ggb/toolbar/mode_mirroratpoint.png[/icon] between the center and each vertex.[/*][*]Use the segment tool [icon]/images/ggb/toolbar/mode_segment.png[/icon] to join the vertices in the way they are joined in the original figure.[br][/*][/list]
Create a scale drawing of triangle ABC about center D and scale factor r = 1/2.
– Katie Acland

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Module 2B Dilations

  • 1. 2.11 Warm-Up - Day 2
  • 2. 2.11 Warm-Up - Day 1
  • 3. 2.10 Activity
  • 4. 2.09 Warm-up
  • 5. 2.08 Warmup
  • 6. 2.07 Warm-up
  • 7. Dilations Part 2: What Do You Notice?
  • 8. Dilations of a star

2.1.

2.11 Warm-Up - Day 2

If Triangle 2 (A'B'C') is a dilation of Triangle 1 (ABC), and Triangle 3 (A''B''C'') is a dilation of Triangle 2, what is the relationship between Triangle 3 and Triangle 1?
Determine the scale factor going from Triangle 1 (ABC) to Triangle 2 (A'B'C'). Take measurements as needed.
Determine the scale factor going from Triangle 2 (A'B'C') to Triangle 3 (A''B''C''). Take measurements as needed.
Determine the scale factor going from Triangle 1 (ABC) to Triangle 3 (A''B''C''). Take measurements as needed.
Do you see a relationship between the value of the scale factor going from Triangle 1 to Triangle 3 and the scale factors determined going from Triangle 1 to Triangle 2, and Triangle 2 to Triangle 3?
– Katie Acland

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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3.

Module 2C Similarity and Dilations

  • 1. 2.17 SSS Similarity Theorem: Exploration
  • 2. SAS Similarity Theorem: Exploration
  • 3. 2.15 Warm-Up - Building Similar Triangles
  • 4. 2.15 Angle-Angle (AA) Similarity Theorem: Quick Investigation
  • 5. Lesson 2.19 - Eratosthenes and the Circumference of the Earth
  • 6. 2.12 Warm-Up

3.1.

2.17 SSS Similarity Theorem: Exploration

Position the triangles anywhere you'd like! Then slide the slider slowly Yet before checking the checkbox that appears (upper left corner), please answer the questions that follow first.
What do you notice about all 3 sides of one triangle when compared with all 3 sides of the other triangle?
Now click the checkbox in the upper left corner. Then slide the slider the rest of the way slowly. What can you conclude about these triangles?
– Katie Acland, Tim Brzezinski

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Module 2D Applying Similarity to Right Triangles

  • 1. 2.21 Special Relationships within Right Triangles
  • 2. Similar Right Triangles (V2)
  • 3. Similar Right Triangles (V1)
  • 4. Pythagorean Theorem Proof, new in 2023
  • 5. Pythagorean Theorem
  • 6. Pythagorean Triples
  • 7. Converse Pythagorean Theorem

4.1.

2.21 Special Relationships within Right Triangles

An altitude of a triangle is a perpendicular line segment from a vertex to the line determined by the opposite side. In [b]△[/b]BCD below, segment BE is the altitude from vertex B to the line containing DC.
How many triangles do you see?
Identify the triangles by name. For example, one triangle is BCD.
Is [color=#ff0000][b]△[/b]BCD[/color] ~ [color=#38761d][b]△[/b]BEC[/color]? If so, name the rule.
Is [color=#ff0000][b]△[/b]BCD [/color]~ [color=#0000ff][b]△[/b]BED[/color]? If so, name the rule.
Is [color=#38761d][b]△[/b]BEC[/color] ~ [color=#0000ff][b]△[/b]BED[/color]? How do we know this to be true?
– Katie Acland

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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5.

Module 2E Trigonometry


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