# Congruent Circles: Definition

[color=#000000]The applet below demonstrates what it means for 2 circles to be [b]congruent circles. [/b] [br]Interact with this applet for a minute or two, then answer the writing prompt that follows. [br][i]Be sure to change the locations of the points around each time before re-sliding the slider.[/i][/color]
Complete the following sentence definition: [br][br]Two circles are said to be congruent circles [color=#1e84cc][b]if and only if...[/b][/color]

# Circle Terminology

[color=#000000]There are many vocabulary terms we use when talking about a circle. [br]The following applet was designed to help you clearly see (and interact) with each term. [br]Mess around with this applet for a few minutes. [br][br][/color][i][b][color=#000000]As you do, be sure to change the locations of the BIG POINTS displayed! [/color][br][br][/b][/i][b][color=#000000]Use this applet to help you author sentence definitions for each of these terms on your [/color][i][color=#0000ff]Circle Terminology [/color][/i][color=#000000]activity sheet given to you at the beginning of class. [/color][/b]

# Circumcircle: Construction Exercise (VA)

[color=#000000]Use any of the tools in the limited toolbar below to construct this triangle's circumcircle. [br][br]You can use the slider to change the measure of angle [i]A[/i] at any time. [br]Feel free to move the triangle's white vertices around as well. [br][br]Feel free to reference [url=https://www.geogebra.org/m/ueV9RpZf]this worksheet[/url] at any time. [/color]
[color=#980000][b]Recall that the circumcenter is the center of a triangle's circumcircle. [br][/b][/color][br][b][color=#000000]Questions: [/color][/b][br][br][color=#000000]1) Is it ever possible for a triangle's circumcenter to lie OUTSIDE the triangle? I[br] If so, under what circumstance(s) will this occur?[br][br]2) Is it ever possible for a triangle's circumcenter to lie ON THE TRIANGLE ITSELF? [br] If so, under what circumstance(s) will this occur? [br] [br]3) If your answer for (2) was "YES", where on the triangle did the circumcenter lie?[br] Use the tools of GeoGebra to validate your response. [br][br][/color][color=#000000]4) Is it ever possible for a triangle's circumcenter to lie INSIDE the triangle? [br] If so, under what circumstance(s) will this occur?[/color]

# Tangent to Circle: Construction 1

[color=#980000][b]Directions: [/b][/color][br][br][color=#000000]Use the limited toolbar in the applet below to construct a line that is tangent to the circle that passes through the [/color][color=#ff00ff][b]PINK POINT.[/b][/color] [color=#000000][br][br]Use the [b]Angle[/b] tool to check the accuracy of your construction afterwards.[/color] [br][br][color=#000000][i]Do not open another tab on your internet browser to look it up either. [br]Think about what you've learned about lines drawn tangent to circles! [/i][/color]

 Try to imagine how you might measure the subtended arc in terms of radius lengths. Once you have taken a guess use the slider to see the unfolded length. Turn on the radius ruler to confirm your guess. Geogebra will measure the angle in terms of radians, but it will restrict the answer on the interval of zero to 2 Pi.

# CCSS HS GEOMETRY RESOURCES!!!

[color=#0000ff]This worksheet contains [/color][color=#980000][b]links[/b][/color][color=#0000ff] to [/color][b]HUNDREDS [/b][b]of dynamic and engaging geometry resources. [/b][b][color=#0000ff]Each worksheet is mapped to 1 (or more) of the standards listed in the [/color][url=http://www.corestandards.org/Math/Content/HSG/introduction/]HIGH SCHOOL: Geometry[/url] [color=#0000ff]section of the [/color][url=http://www.corestandards.org/Math/]Common Core State Standards Initiative for Mathematics[/url][color=#980000]. [/color][color=#274e13] [br][/color][/b][br][color=#980000][b]LINKS: [br][/b][/color][br][url=https://www.geogebra.org/m/z8nvD94T#chapter/0]CCSS High School: Geometry (Congruence) Volume 1[/url][br][br][url=https://www.geogebra.org/m/munhXmzx#chapter/0]CSSS High School: Geometry (Congruence) Volume 2[/url][br][br][url=https://www.geogebra.org/m/dPqv8ACE#chapter/0]CCSS High School: Geometry (Similarity, Right Triangles, & Trigonometry)[/url] [br][br][url=https://www.geogebra.org/m/C7dutQHh#chapter/0]CCSS High School: Geometry (Circles)[/url][br][br][url=https://www.geogebra.org/m/K2YbdFk8#chapter/0]CCSS High School: Geometry (Expressing Geometric Properties with Equations)[/url][br][url=https://www.geogebra.org/m/xDNjSjEK#chapter/0][br]CCSS High School: Geometry (Geometric Measurement & Dimension)[/url][br][br][url=https://www.geogebra.org/m/pptbYhsy#chapter/0]CCSS High School: Geometry (Modeling with Geometry)[/url]﻿[br][br][b][color=#0000ff]*NEW![/color][/b] [url=https://www.geogebra.org/m/NjmEPs3t]CCSS High School: Geometry (Higher Level Enrichment Challenges)[/url]
##### SAMPLE 2: What 2 theorems are dynamically being illustrated below? (Feel free to move the white points wherever you'd like.)
[color=#000000]Teachers can use these resources as a powerful means to naturally [br][br][/color][b][color=#0000ff]1) Foster Discovery Learning[br][/color][color=#0000ff]2) Provide Meaningful Remediation[br]3) Differentiate Instruction, &[br]4) Assess students' understanding.[/color][color=#000000] [/color][/b][br][br][color=#000000]Since any curriculum is [/color][b][i][color=#980000]always[/color][/i][/b][color=#000000] a fluid document, these books, too, will continue to remain works in progress.[/color][br][br][b][color=#0000ff]Teachers:[/color][/b][color=#000000] [br]It is my hope that these resources help empower your students to actively (and regularly) discover the fascinating world of mathematics around them. [br][/color][br][b][color=#0000ff]Students:[/color][/b][color=#000000] [br]It is my hope that these resources help you discover & help reinforce mathematics concepts in a way that makes sense to you. [/color]
[b][color=#980000]These GeoGebra books display the amazing work from several esteemed members of the GeoGebra community. I am truly humbled and amazed by their talents. These comprehensive resources would not have been possible without their contributions. [br][br]I would like to express a [u]HUGE THANK YOU[/u] to[br][br][/color][/b][url=https://www.geogebra.org/orchiming]Anthony C.M. OR[/url][br][url=https://www.geogebra.org/stevephelps]Steve Phelps[/url][br][url=https://www.geogebra.org/jennifer+silverman]Jennifer Silverman[/url][br][url=https://www.geogebra.org/tedcoe]Dr. Ted Coe[/url][br][url=https://www.geogebra.org/scruz10]Samantha Cruz[/url][br][url=https://www.geogebra.org/tlindy]Terry Lee Lindenmuth[br][/url][url=https://www.geogebra.org/ra%C3%BAl+falc%C3%B3n]Raul Manuel Falcon Ganfornina[/url] [br][url=https://www.geogebra.org/walch+education]Walch Education[/url]﻿[br][url=https://www.geogebra.org/edc+in+maine#]EDC in Maine[/url][br][br]For questions, suggestions, and/or comments, feel free to e-mail me at any time. [br]I wish you much success in your journey of teaching and/or learning mathematics! [br][br]Best,[br][br][url=https://www.geogebra.org/tbrzezinski]Tim Brzezinski[br][br][/url][color=#1e84cc]Independent Mathematics Education Consultant ([url=http://www.dynamicmathsolutions.com/]Dynamic Math Solutions[/url])[br][/color][color=#1e84cc]Adjunct Mathematics Instructor at Central Connecticut State University[br]Former High School Mathematics Teacher (15 years) at Berlin High School (CT, USA)[/color][br][br]E-Mail: dynamicmathsolutions@gmail.com [br]Twitter: [url=https://twitter.com/dynamic_math]@dynamic_math[/url][br]

# CCSS HS FUNCTIONS RESOURCES!!!

﻿This worksheet currently contains [color=#0000ff][b]links[/b][/color] to [b]over 150 [/b][b]DYNAMIC and ENGAGING resources pertaining to FUNCTIONS. [/b][b]Each worksheet is mapped to 1 (or more) of the standards listed in the[color=#0000ff] [url=http://www.corestandards.org/Math/Content/HSF/introduction/]CCSS High School: Functions[/url]﻿ [/color][/b]section of the[b] [color=#cc0000][url=http://www.corestandards.org/Math/]Common Core State Standards Initiative for Mathematics[/url].[/color][/b][color=#666666][b] [/b][br][br][/color][color=#980000][b]LINKS: [br][/b][/color][br][url=https://www.geogebra.org/m/k6Dvu9f3]CCSS High School: Functions (Interpreting Functions)[/url]﻿[br][br][url=https://www.geogebra.org/m/uTddJKRC]CCSS High School: Functions (Building Functions)[/url][br][br][url=https://www.geogebra.org/m/GMvvpwrm]CCSS High School: Functions (Linear, Quadratic, & Exponential Models)[/url][br][br][url=https://www.geogebra.org/m/aWuJMDas]CCSS High School: Functions (Trigonometric Functions)[/url][br][br][br][color=#000000]Teachers can use these resources as a powerful means to naturally [br][br][/color][b][color=#0000ff]1) Foster Discovery Learning[br][/color][color=#0000ff]2) Provide Meaningful Remediation[br]3) Differentiate Instruction, &[br]4) Assess students' understanding.[/color][color=#000000] [br][br][/color][/b][color=#000000]Since any curriculum is [/color][b][i][color=#0000ff]always[/color][/i][/b][color=#000000] a fluid document, these books, too, will continue to remain works in progress. More items will continue to be added to these volumes. [br][/color]
##### Sample 2 - ODD FUNCTION ILLUSTRATOR: Feel free to move any of the BIG points wherever you'd like.
[b][color=#0000ff]Teachers:[/color][/b][color=#000000] [br]It is my hope that these resources help empower your students to actively (and regularly) discover the fascinating world of mathematics around them. [br][br][/color][b][color=#0000ff]Students:[/color][/b][color=#000000] [br]It is my hope that these resources help you discover & help reinforce mathematics concepts in a way that makes sense to you.[br][br][/color][b]I would like to express a HUGE THANK YOU to[/b] [url=https://www.geogebra.org/orchiming][color=#0000ff]Anthony C.M.Or[/color][/url] [b]and[/b] [color=#0000ff][url=https://www.geogebra.org/stevephelps]Steve Phelps[/url], [/color][br][b]whose work also appears in this project. [/b][br][br]For questions, suggestions, and/or comments, feel free to e-mail me at any time. [br]I wish you much success in your journey of teaching and/or learning mathematics! [br][br]Best,[br][br][url=https://www.geogebra.org/tbrzezinski]Tim Brzezinski[br][/url][color=#1e84cc][br]Independent Mathematics Education Consultant ([url=http://www.dynamicmathsolutions.com/]Dynamic Math Solutions[/url])[br][/color][color=#1e84cc]Adjunct Mathematics Instructor at Central Connecticut State University[br]Former High School Mathematics Teacher (15 years) at Berlin High School (CT, USA)[/color][br][br]E-Mail: dynamicmathsolutions@gmail.com [br]Twitter: [url=https://twitter.com/dynamic_math]@dynamic_math[/url]