Geometry

Lea Rauh, Mar 4, 2025

Table of Contents

  1. 2D Shapes
    1. Geometry 2D - Shapes Activity
    2. 2D shapes bingo
    3. 2D shapes
    4. Discover 2D shapes- NETS!
  2. Area
    1. Geometry Resources
    2. Area of 2d Shapes
    3. Parallelogram: Area
    4. Area of a Sector
    5. Square Area
    6. Rectangle Area
  3. Volume
    1. Volume of cone
    2. Volume of Spheres
    3. 521 - Volume Game
    4. volume
    5. Volume of cylinder
    6. Volume: Intuitive Introduction
  4. Surface Area
    1. Surface Area: Introductory Exercises
    2. 514 - Surface Area Game
    3. Surface Area Problems
    4. Surface Area & Volume: Right Prism
  5. Lines
    1. Basic Terms in Geometry
    2. Parallel & Perpendicular Lines
    3. Parallel Lines Definition
  6. Angles
    1. Vertical Angles Exploration (2)
    2. Open Middle: Supplementary Angles
    3. Interior Angles in Polygons Exploration
  7. Perimeter
    1. Perimeter and Area
    2. 407 - Perimeter
    3. Perimeter Practice
    4. GeoBoard - Arrays, area, perimeter, and representations

1.

2D Shapes

  • 1. Geometry 2D - Shapes Activity
  • 2. 2D shapes bingo
  • 3. 2D shapes
  • 4. Discover 2D shapes- NETS!

1.1.

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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2.

Area

  • 1. Geometry Resources
  • 2. Area of 2d Shapes
  • 3. Parallelogram: Area
  • 4. Area of a Sector
  • 5. Square Area
  • 6. Rectangle Area

2.1.

Geometry Resources

[list][*][b][url=https://www.geogebra.org/m/z8nvD94T]Congruence (Volume 1)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/munhXmzx]Congruence (Volume 2)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/dPqv8ACE]Similarity, Right Triangles, Trigonometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/C7dutQHh]Circles[/url][/b][/*][*][b][url=https://www.geogebra.org/m/K2YbdFk8]Coordinate and Analytic Geometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/xDNjSjEK]Area, Surface Area, Volume, 3D, Cross Section[/url] [/b][/*][*][b][url=https://www.geogebra.org/m/NjmEPs3t]Proof Challenges[/url]  [/b][/*][/list]
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
– Tim Brzezinski

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3.

Volume

  • 1. Volume of cone
  • 2. Volume of Spheres
  • 3. 521 - Volume Game
  • 4. volume
  • 5. Volume of cylinder
  • 6. Volume: Intuitive Introduction

3.1.

Volume of cone

The text book definition of pyramid and cone are given below.
[br][table][tr][td]Pyramid[br][/td][td]Cone[br][/td][/tr][tr][td]Pyramid is a solid formed by polygon base and all other triangles faces with a common vertex.[br][/td][td]Cone is a solid formed by circular base and rays emanating from a fixed point (vertex) and passing through the base.[br][/td][/tr][tr][td]In the limit, as the number of faces approaches infinity, the shape is a cone.[br][/td][td]There are four types of cones: circular, elliptical, right, and oblique.[br]In the figure left, keep sliding the number of sides and see that as the number of triangular faces increases, the pyramid begins to look more and more like a cone.[br][br]So, a cone is also a pyramid, and its fifth type is n = ∞.[br][/td][/tr][/table]
In the assumption as explained above, we can understand cone as a pyramid with circular base.[br]In the premises, the volume of cone is[br]              V= 1/3 * B* h[br]However,[br]We can also use cavalieri's principle to find the volume of cone. [br][br]Cavalieri's principle[br]If area of cross sections at parallel heights of two solids and their volume are proportional. [br][br]दुईवटा solids लाई उही उचाईबाट parallel plane ले काट्दा बन्ने cross sections को area र ति दुईवटा solids को volume समानुपातिक हुनेछ। [br][br]वा[br][br]दुईवटा solids लाई उही उचाईबाट parallel plane ले काट्दा बन्ने cross sections को area बराबर भएमा ति दुईवटा solids को volume पनि बराबर हुनेछ।
Volume of Cone: Proof
नेपाली version
– Bed Prasad Dhakal

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4.

Surface Area

  • 1. Surface Area: Introductory Exercises
  • 2. 514 - Surface Area Game
  • 3. Surface Area Problems
  • 4. Surface Area & Volume: Right Prism

4.1.

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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5.

Lines

  • 1. Basic Terms in Geometry
  • 2. Parallel & Perpendicular Lines
  • 3. Parallel Lines Definition

5.1.

Basic Terms in Geometry

This lessons reviews Basic Geometry Vocabulary with interactive displays of the vocabulary.[br][br]Point(s), Plane, Line, Segment, Ray, Angle, Side(s), Vertex, etc.
Additional resources to view:[br]Standard Position 01[br]Standard Position 01a[br]Coterminal Angles 01b
– Auston B Cron

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6.

Angles

  • 1. Vertical Angles Exploration (2)
  • 2. Open Middle: Supplementary Angles
  • 3. Interior Angles in Polygons Exploration

6.1.

Vertical Angles Exploration (2)

Interact with this app below for a minute. Then answer the questions that follow.
Use the ANGLE tool to measure a pair of colored angles. What do you notice?
Measure the other two angles you see now. What do you notice?
Now that you have all four angle measures displayed, drag the slider around. What can you conclude about each pair of vertical angles?
– Tim Brzezinski

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7.

Perimeter

  • 1. Perimeter and Area
  • 2. 407 - Perimeter
  • 3. Perimeter Practice
  • 4. GeoBoard - Arrays, area, perimeter, and representations

7.1.

Perimeter and Area

10.1 Perimeter
[b][color=#ff0000]10.1 Perimeter[/color][color=#0000ff][br][br]How do you determine the perimeter?[/color][/b][br][i][color=#0000ff][size=85]Bagaimana anda menentukan perimeter?[/size][/color][/i]
[b][color=#0000ff]Perimeter is the total length around an enclosed area.[/color][/b][br][color=#0000ff][size=85]Perimeter ialah jumlah ukuran panjang sisi yang mengelilingi suatu kawasan tertutup.[/size][/color]
[b][color=#0000ff]Which Object has the largest perimeter.[/color][/b][br][br]A) I[br]B) II[br]C) III[br]D) IV
Largest perimeter is Object:[br]Perimeter terbesar adalah Objek:[br][br][br]Reason:
Select the distance or length [icon]/images/ggb/toolbar/mode_distance.png[/icon]tool. Find the perimeter of each of the following shapes.
[b][color=#ff0000]Which Object has the largest perimeter?[/color][/b]
[b][color=#ff0000]Draw an quadrilateral with perimeter 18 cm[br][/color][/b]Lukiskan rajah Sisi Empat yang berperimeter 18 cm
Draw an quadrilateral with perimeter 18 cm
[b][color=#ff0000]Draw a triangle with perimeter 18 cm[br][/color][/b]Lukiskan rajah segitiga yang berperimeter 18 cm
Draw a Triangle with Perimeter 18 cm
Circle
Use the Polygon [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool and estimate the perimeter of circle given
Perimeter (Circumference) of Circle
Perimeter of Circle is
– Rajinder Singh TutorRaj

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Information