Now that you have notes on the different types of angles made by a transversal, find the missing angle measures.
2-D Geometry
This is a collection of interactive examples of various plane geometry visuals, both 2D and 3D.
Inhaltsverzeichnis
- Angles
- Types of Angles
- Complementary Angles Meaning
- Exploring Complementary Angles
- Supplementary Angles Meaning
- Vertical Angles Theorem
- Vertical Angles Exploration (2)
- Same Side Interior Angles and Parallel Lines
- Alternate Interior Angles
- Alternate Interior Angles and Parallel Lines
- Same Side Exterior Angles and Parallel Lines
- Interior Angles in Polygons Exploration
- Sum of Interior Angles of a Polygon
- Polygons: Exterior Angles - REVAMPED
- Alternate Exterior Angles and Parallel Lines
- Lambourghini Turning Angles
- Exterior Angles of Polygons
- Polygons -- Areas
- Area of a Rectangle
- Rectangle Area
- Square Area
- AREA OF SQUARE
- Triangle Area Action! (V1)
- Parallelogram: Area
- Parallelogram Area
- Area of a Rhombus
- Trapezoid: Area (I)
- Triangle Area Action!!! (V2)
- Solids -- Surface Area
- Surface Area: Introductory Exercises
- The Surface Area of Cylinder
- Volumes
- Volumes of Rectangular Prisms
- Volumes of Rectangular Prisms
- Volume of a Rectangular Prism
- Volumes of Cubes and Prisms
- Volume of a Cylinder and Pyramid Investigation
- Exploring Volume of a Cylinder
- G.GGMD.3 Volume of a cylinder
- Voluem of Pyramid ( Method I )
- Volume of Pyramid
- Circles and Spheres
- 8.2 Area of Circles
- Area of Circles
- Area of a Circle - without words (Animation 38)
- Volume Of Sphere
- Volume of a Sphere
- Sphere Surface Area #1
- Surface area of a sphere
Types of Angles
Complementary Angles
1) What do you notice about the two angles when you slide the two sliders? What do complementary angles add up to?
Supplementary Angles
2) What do you notice about these two angles? What do supplementary angles add up to?
Hmmm.....
[size=150][color=#0000ff]3) What is the complementary angle to 38[/color][math]^\circ[/math][color=#0000ff]?[br][br][br][br]4) What is the supplementary angle to 38[/color][math]^\circ[/math][color=#0000ff]?[br][br][br][br]5) Is it possible for one angle of a pair of complementary angles to be 100[/color][math]^\circ[/math][color=#0000ff]? Why or why not?[br][/color][/size]
Vertical Angles
Vertical angles are angles that are across from each other when two lines intersect.[br][br]6) What do you notice about the angle measures of vertical angles?[br]
Transversal
A [u]transversal[/u] is a line that intersects two parallel lines.[br][br]7) First check the "Show Corresponding Angles" box. What do you notice as you slide the first slider? Corresponding angles are in the SAME SPOT on different parallel lines. On your paper write, "Corresponding angles are in the same spot on different parallel lines."[br][br]8) Now, check the "Show Alternate Interior Angles" box. What do you notice as you slide the first slider? Alternate Interior Angles show the opposite angles on the inside of parallel lines. They have the same angle measure. On your paper, write how you will remember Alternate Interior Angles.[br][br]9) Lastly, check the "Show Alternate Exterior Angles" box. What do you notice as you slide the first slider? Alternate Exterior Angles show the opposite angles on the outside of the parallel lines. They have the same angle measure. On your paper, write how you will remember the difference between Alternate Interior Angles and Alternate Exterior Angles.[br][br]
Example!
10) [br]m[math]\angle[/math]1 =[br]m[math]\angle[/math]2=[br]m[math]\angle[/math]3=[br]m[math]\angle[/math]4=[br]m[math]\angle[/math]5=[br]m[math]\angle[/math]6=[br]m[math]\angle[/math]7=[br]
Area of a Rectangle
In this worksheet you will investigate the area of a rectangle.
Investigation:[br][br]1) Move the sliders Base and Height and describe what happens to the image.[br][br] 2) What relationship does the number of squares have with the area of the rectangle?[br][br] 3) Is there a way to find the number of square with out counting them?[br][br] 4) What conjecture can you make about the formula for area of a rectangle?
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.
Volumes of Rectangular Prisms
Explore.
Practise
What happens to the volume when you double the height?
Can you find dimensions so that the prism's volume is exactly 72 cubic units? Show at least two different combinations.
Can you make two different rectangular prisms (different ℓ, w, h) that both have volume = 120 cubic units? List as many as you can.
8.2 Area of Circles
area of circle