Geometry Booklet

Jayden Jones, Mar 4, 2025

Covering area, volume, perimeter, angles, and more for 2d and 3d shapes.

Table of Contents

  1. Area
    1. Area Of A Triangle
    2. Areas of Squares and Right Triangles
    3. Parallelogram: Area
    4. Trapezoid: Area (I)
    5. 11_03_Geogebra area of quadrilateral
  2. Surface Area
    1. Surface Area: Introductory Exercises
    2. Surface Area & Volume: Right Prism
    3. 514 - Surface Area Game
    4. Surface Area of Spheres
    5. Curved Surface Area of Cones (Parametric Curved Surface)
    6. Surface Area - Trapezoid
  3. Volume
    1. Volume Balok
    2. Volume of Spheres
    3. Volume of cone
    4. Sphere (Volume + Surface)
    5. Volume and Area of Cylinder gt2e
    6. Volume Similarity
  4. 2D Shapes
    1. Geometry 2D - Shapes Activity
    2. 2D shapes
    3. Translation of 2D shapes by a given translation Vector
    4. Reflect 2D shapes (triangle)
  5. Angles
    1. Polygons: Exterior Angles
    2. Vertical Angles Theorem
    3. Supplementary Angles (Quick Exploration)
    4. Adjacent Angles
    5. Triangle Interior and Exterior Angles: Quick Exploration
  6. Lines
    1. Parallel Lines Proportionality Theorem
    2. Perpendicular Lines: Quick Intro
    3. Open Middle: Equations of Parallel Lines
    4. Graph the Line
    5. Investigating Parallel and Perpendicular Lines
  7. Perimeter
    1. Perimeter & Circumference
    2. Regular Polygons: Perimeter & Area
    3. Triangle: Area and Perimeter
    4. Perimeter Rectangles
    5. Perimeter Practice

1.

Area

  • 1. Area Of A Triangle
  • 2. Areas of Squares and Right Triangles
  • 3. Parallelogram: Area
  • 4. Trapezoid: Area (I)
  • 5. 11_03_Geogebra area of quadrilateral

1.1.

Area Of A Triangle

Discovering the Area of a Triangle
In this activity, you will investigate how to find the area of a triangle.
Follow the directions below to investigate how to find the area of a triangle.
Investigation:[br]1) Adjust the base slider so that the base is 10 units. [br][br]2) Move point D so that the triangle is a right triangle and note the area of the triangle.           [br][br]3) Move the "Hint" slider and identify the new figure. Answer the questions below.
Question 1
What figure was created after you moved the "Hint" slider?
Question 2
What is the area of the new figure that was created when moving the slider?
Investigation:[br][br]1) Make sure the base slider is still located at 10 units. [br][br]2) Move point D to make an obtuse triangle and note the area of the triangle.                         [br]3) Move the "Hint" slider and identify the new figure. Answer the question below.
Question 3
What figure was created after you moved the "Hint" slider?
Question 4
What is the area of the new figure that was created when moving the slider?
Investigation:[br][br]1) Adjust the base slider so that the base is 10 units. [br][br]2) Move point D so that the triangle is an acute triangle and note the area of the triangle.                          [br]3) Move the "Hint" slider and identify the new figure. Answer the questions below.
Question 5
What figure was created after you moved the "Hint" slider?
Question 6
What is the area of the new figure that was created when moving the slider?
Question 7
What conclusion can you make based on the area of of the new figures and the area of the three triangles?
Question 8
Your Turn:[br]1) Change the height and the base using values of your choosing. [br]2) Create a right, obtuse, and acute triangle using your chosen base and height.[br]3) Compare the areas.[br][br]How does the area of the quadrilaterals compare to the area of the triangles? Why do you think this is so?
– Jennifer Mallory, GeoGebra Materials Team

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2.

Surface Area

  • 1. Surface Area: Introductory Exercises
  • 2. Surface Area & Volume: Right Prism
  • 3. 514 - Surface Area Game
  • 4. Surface Area of Spheres
  • 5. Curved Surface Area of Cones (Parametric Curved Surface)
  • 6. Surface Area - Trapezoid

2.1.

Surface Area: Introductory Exercises

Take a few minutes to interact with the rectangular prism shown here. After doing so, create one that has a length = 4 units, width = 5 units, and height = 3 units.
How many square units (i.e. "squares") appear on 1 [b][color=#ff00ff]pink face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b][color=#bf9000]gold face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b]white face[/b]?
Use your answers for (1) to determine the TOTAL SURFACE AREA of this rectangular prism. [br]That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?
Now create a rectangular prism that has a length = 8 units, width = 3 units, and height = 5 units.
How many square units (i.e. "squares") appear on 1 [b][color=#ff00ff]pink face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b][color=#bf9000]gold face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b]white face[/b]?
Use your answers for (3) to determine the TOTAL SURFACE AREA of this rectangular prism. [br]That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?
Overall, how we can determine the total surface area (number of squares) that cover the entire surface of a rectangular prism? Describe.
– Tim Brzezinski

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3.

Volume

  • 1. Volume Balok
  • 2. Volume of Spheres
  • 3. Volume of cone
  • 4. Sphere (Volume + Surface)
  • 5. Volume and Area of Cylinder gt2e
  • 6. Volume Similarity

3.1.

Volume Balok

Menemukan Rumus Volume Balok
Geser slider p, l, dan t agar balok hijau dipenuhi oleh kubus-kubus satuan.[br]Amati banyak kubus satuan yang mengisi balok.[br]Kalian akan menemukan hubungan antara volume balok (V) dengan p, l, dan t.[br][br]klik kanan - drag untuk memutar objek dimensi tiga.[br]
Langkah Pembuatan
– Untung Trisna S.

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4.

2D Shapes

  • 1. Geometry 2D - Shapes Activity
  • 2. 2D shapes
  • 3. Translation of 2D shapes by a given translation Vector
  • 4. Reflect 2D shapes (triangle)

4.1.

Geometry 2D - Shapes Activity

The purpose of this activity is to give students the opportunity to discover that 2D-shapes are all around us. Students will also be able to identify 2D-shapes.
Directions for teachers:[br]Allow students to preview the video on 2D-shapes. [br]Allow students to identify the 2D-shapes in the image. Allow students to use the tools provided to trace over all the 2D-shapes on the image that they see. Students will also name the shapes and write the number of each 2D-shape found.
– Vernet Longville

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5.

Angles

  • 1. Polygons: Exterior Angles
  • 2. Vertical Angles Theorem
  • 3. Supplementary Angles (Quick Exploration)
  • 4. Adjacent Angles
  • 5. Triangle Interior and Exterior Angles: Quick Exploration

5.1.

Polygons: Exterior Angles

The exterior angles of a triangle, quadrilateral, and pentagon are shown, respectively, in the applets below. [br][br]You can control the size of a colored exterior angle by using the slider with matching color. [br]Feel free to move the vertices of these polygons anywhere you'd like. [br][br][b]Note:[/b] [br]For the [b]quadrilateral[/b] & [b]pentagon[/b], the last two applets work best if these polygons are kept [b]convex.[/b][br]If you don't remember what this term means, [url=https://www.geogebra.org/m/knnPDMR3]click here for a refresher[/url].
Exterior Angles of a Triangle
Exterior Angles of a Quadrilateral
Exterior Angles of a Pentagon
What do you notice? What is common about the measures of the exterior angles of any one of these polygons?
Do you think what you've observed for the triangle, quadrilateral, and pentagon above will also hold true for a hexagon, heptagon, and octagon? [br][br]Create a new GeoGebra file and do some investigating to informally test your hypotheses!
– Tim Brzezinski

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6.

Lines

  • 1. Parallel Lines Proportionality Theorem
  • 2. Perpendicular Lines: Quick Intro
  • 3. Open Middle: Equations of Parallel Lines
  • 4. Graph the Line
  • 5. Investigating Parallel and Perpendicular Lines

6.1.

Parallel Lines Proportionality Theorem

[color=#000000]This applet accompanies the [/color][color=#0000ff][b]Parallel Lines Proportionality Theorems [/b]activity worksheet[/color][color=#000000] given to you at the beginning of class. [br][br][/color][b][color=#000000]Teachers: [/color][/b][b][color=#cc0000]A PDF copy of this lesson activity can be found below the applet. [/color][/b]
Parallel Lines Proportionality Theorem
– Tim Brzezinski

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7.

Perimeter

  • 1. Perimeter & Circumference
  • 2. Regular Polygons: Perimeter & Area
  • 3. Triangle: Area and Perimeter
  • 4. Perimeter Rectangles
  • 5. Perimeter Practice

7.1.

Perimeter & Circumference

Introduction
[size=150][color=#ff00ff]Perimeter [/color]is defined as the distance around a two-dimensional shape. [color=#0000ff]Circumference [/color]is what we call the perimeter of a circle. We can use [color=#ff00ff]perimeter [/color]and [color=#0000ff]circumference [color=#000000]to find the distances around everyday objects like houses, gardens, and pools.[br][br]In this worksheet you will find the [color=#ff00ff]perimeter [color=#000000]of different objects and you will see how the length of the radius of a circle affects the [color=#0000ff]circumference.[/color][/color][/color][/color][/color][/size]
Perimeter Formulas
The perimeter of squares, rectangles, triangles, and other non-circular shapes can be found by adding the sides together, too!
Find the perimeter of...
Susie wants to plant a rectangular garden. The length of the garden will be 7 feet and the width will be 4.5 feet. What is the perimeter in feet?
Below is a circle with a marked center and a point on the circle. A'A (f) is the radius. Using the slider, you can adjust the size of the circle, which in turn, adjusts the [color=#0000ff]circumference[/color]. [br][br]Find the [color=#0000ff]circumference [color=#000000]if the ratio = 2.5.[/color][/color][br][br]If the ratio = 2, the radius = 2.78 units.
Circumference
Circumference
If the ratio = 2.5, what is the circumference of the circle?
Triangle Perimeter
Move the slider to adjust the lengths of the triangle. The increasing lengths will increase the perimeter value.[br][br]What is the perimeter of Triangle CDE when the ratio =-1.75?
Quiz
What is the formula for circumference of a circle?
Pool Perimeter
Jay wants to know the perimeter of his new pool. If the pool is a rectangle, and the width is 6 m and the length is 10 m, what is the perimeter?
Rachel's new puzzle is a square. One side length is 12 inches. What is the perimeter?
– Sarah Fryman

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Information