Dilation Introduction: Transformers!

Explore this applet to see how the center of dilation and the scale factor affect the image.
Turn off the images and explore the way the lines change. What do you notice?

Similar Figures: Dynamic Illustration

[b]DEFINITION:[br][br]ANY 2 figures are said to be SIMILAR FIGURES if and only if one can be mapped perfectly onto the other under a single transformation OR a composition of 2 or more transformations. [br][br][/b]The applet below dynamically illustrates what it means, by definition, for any 2 triangles to be similar. [br]Feel free to move any of the white vertices anywhere you'd like. [color=#38761d][b]You can also change the size of the green triangle by moving the green slider. [/b][/color]

Angle-Angle (Investigation)

[b]Students:[br][/b][br]Please use the GeoGebra task applet below to complete the [b]Angle-Angle (Investigation) [/b]given to you at the beginning of class. [br][br][b]LINK:[/b] [b][color=#0000ff][url=https://docs.google.com/document/d/10gizSV-6UM_E6amlcEYLmVmnWgqpW_jWti6MYAyoSwk/edit?usp=sharing]Angle-Angle (Investigation)[/url][/color] [/b][br][br][b][color=#0000ff]When done, don't forget to select the [/color][color=#ff7700]SUBMIT/TURN IN[/color][color=#0000ff] button! [/color][/b]

SAS ~ Theorem

[color=#000000]In the applet below, you'll find two triangles.  [br][br]The [b]black angle[/b] in the [/color][color=#38761d][b]green triangle[/b][/color] [b][color=#000000]is congruent to[/color][/b][color=#000000] the [/color][b][color=#000000]black angle[/color][/b][color=#000000] in the [/color][b][color=#ff00ff]pink triangle[/color][/b][color=#000000]. [/color][br][br][color=#000000]In the [/color][color=#38761d][b]green triangle[/b][/color][color=#000000], the [b]black angle is the included angle between sides [/b][/color][b][i][color=#000000]a[/color][/i][color=#000000] and [/color][i][color=#000000]b[/color][/i][/b][color=#000000].  [/color][br][color=#000000]In the [/color][b][color=#ff00ff]pink triangle[/color][/b][color=#000000], the [b]black angle is the included angle between sides [i]ka[/i] and [i]kb[/i][/b].  [/color][br][br][color=#000000]Interact with the applet below for a few minutes. [/color][color=#000000]As you do, be sure to move the locations of the [/color][color=#38761d][b]green triangle's[/b][/color][color=#000000] [b]BIG BLACK VERTICES[/b] and the location of the [b]BIG X[/b].[br][/color][color=#000000]You can also adjust the value of [/color][i][color=#000000]k[/color][/i][color=#000000] by using the slider or by entering a value between 0 & 1. [/color][color=#000000] [br][/color][color=#000000] [/color][br] 
[color=#000000]Notice how these two triangles have 2 pairs of corresponding sides that are in proportion. (After all, as long as [br]a > 0 & b > 0, ka/a = k and kb/b = k, right?  )  [br][br]The [b]BLACK ANGLES INCLUDED[/b] between these two sides [b]ARE CONGRUENT[/b] as well.  [/color][br][br][b][color=#0000ff]From your observations, what can you conclude about the two triangles?  Why can you conclude this?[br]Clearly justify your response!  [/color][/b]

Quiz: Pythagorean Theorem (1)