IM Geometry (Vasicek ggb files)
Table of Contents
- im.g.1.01.2-3 Build It
- im.g.1.1.2.Illegal Construction Moves with Tools
- im.g.1.1.3 Can You Make A Perfect Copy?
- (Part 2) Can You Make a Perfect Copy?
- im.g.1.03.1. Perpendicular Bisectors
- Find all the points!
- What? Where?
- im.g.1.3.4.Walk The Line
- im.g.1.04.2 Equilateral Triangles
- im.g.1.4.2.What Polygons Can You Find?
- im.g.1.05.2 Make It Right
- im.g.1.5.2.Make It Right
- im.g.1.05.3 Bisect This
- Bisect This (Part 1)
- 1.5.3 Bisect This (Part 2)
- 1.5.3 Bisect This (Part 3)
- im.g.1.06.2 On the Shoulders of Giants
- im.g.1.06.2.Standing On the Shoulders of Giants
- im.g.1.09.2 Who is closest?
- im.g.1.9.2.Who is closest?
- im.g.1.9.04.Another Layer
- im.g.1.9.4.Another Layer (version 1)
- im.g.1.9.4.Another Layer (version 2)
- im.g.1.9.4.Another Layer (version 3)
im.g.1.1.2.Illegal Construction Moves with Tools
1. Create a circle centered at A with radius AB.[br][br]2. Estimate the midpoint of segment AB and label it C.[br]When you create a point in this applet, there will not be a label. [br]To create a label, select the point, then click on the Style Bar. [br]Change the label of the point to C. Be sure to check the box "Show Label."[br][br]3. Create a circle centered at B with radius BC. This creates 2 intersection points. [br]Label the one toward the top of the page as D and the one toward the bottom as E.[br][br]4. Connect points A, D, and E using the polygon tool to make triangle ADE.[br][br]5. Try doing the DRAG TEST. (This is where you try to move each of the points to see if the drawing is a true construction, where it retains its properties).
6. Why do you think that the title of this is "Illegal Construction Moves." [br]What was it supposed to be a construction of, and what about the steps you followed caused it to fail the drag test?
Attribution
illustrative mathematics. geometry. unit 1. lesson 1. activity 2. "Illegal Construction Moves."[br][url=https://im.kendallhunt.com/HS/teachers/2/1/1/index.html]https://im.kendallhunt.com/HS/teachers/2/1/1/index.html[br][/url]Licensed under the Creative Commons Attribution 4.0 license, [br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url]
Find all the points!
Here are 2 points labeled A and B, and a line segment, CD.
1. Find 5 points that are a distance, CD, away from point A.[br]How could you describe all points that are a distance of CD away from point A?
2. Now find 5 points that are a distance, CD, away from point B.[br][br]3. Mark all the points that are a distance of CD away from both A and B [i]at the same time![/i]
im.g.1.4.2.What Polygons Can You Find?
Here is a straightedge and compass construction of a regular hexagon inscribed in a circle, just before the last step of drawing the sides.[br][br]Use the polygon tool in the applet to draw at least 2 polygons on the figure. [br]The vertices of your polygon should be intersection points in the figure.[br]Change the color of your polygons.[br][br]When done, return to write at least 2 conjectures about the polygons you made.
[size=50][color=#6aa84f]Sentence frames: “I notice that __”, “I know ___ because ___”, and “That could/couldn’t be true because ___.”[/color][/size][br]
Attribution
illustrative mathematics. geometry. unit 1. section 4. activity2.[br]"What polygons can you find?"[br][url=https://im.kendallhunt.com/HS/teachers/2/1/4/index.html]https://im.kendallhunt.com/HS/teachers/2/1/4/index.html[/url][br]Licensed under the Creative Commons Attribution 4.0 license[br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url]
im.g.1.5.2.Make It Right
Here is line, [i]l[/i], with point C on the line. [br]Use the compass and straightedge tools on this applet to [br]construct a line perpendicular to line [i]l[/i] that passes through point C.
Attribution
illustrative mathematics. geometry. unit 1. section 5. activity 2. "Make it right."[br][url=https://im.kendallhunt.com/HS/teachers/2/1/5/index.html]https://im.kendallhunt.com/HS/teachers/2/1/5/index.html[br][/url]Licensed under the Creative Commons Attribution 4.0 license[br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url][br]
Bisect This (Part 1)
1.5.3 Part 1
1. Estimate the location of a point, D, so that angle DBA is approximately congruent to angle CBD.[br][br]2. Measure angles DBA and CBD with the angle measurement tool.[br][br]3. Check your results by doing a DRAG TEST. (This is where you try to drag each of the points. If the construction stays true, it works; if the construction doesn't stay true, it fails and is not a good construction.) [br]
When you create ray BD in this manner, you see that ray BD is NOT a true angle bisector.[br]Explain in sentences why this method doesn't work.[br][br]Sentence Frame: "This method doesn't work because ___."
im.g.1.06.2.Standing On the Shoulders of Giants
Here is a line, [i]m[/i], and a point, C, not on the line.[br][br]Use construction moves (straightedge and compass -- tools in the applet) to construct[br]a line perpendicular to line [i]m[/i] that passes through point C.[br][br]Check that it passes the drag test. [br]Be prepared to share your reasoning.
Attribution
illustrative mathematics. geometry. unit 1. lesson 6. activity 2.[br]"Standing On the Shoulders of Giants"[br][url=https://im.kendallhunt.com/HS/teachers/2/1/6/index.html]https://im.kendallhunt.com/HS/teachers/2/1/6/index.html[br][/url]Licensed under the Creative Commons Attribution 4.0 license[br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url][br]
im.g.1.9.2.Who is closest?
Here is a city with three locations of the same store.
1. The company wants to break the city down into regions so that whenever someone orders from an address, their order is sent to the store closest to their home. They have hired you to decide how to partition the city between the 3 stores.
Use the applet above to make the partitions. Then, explain your reasoning.
2. If there are 100 employees, how should they be distributed among the 3 locations? Again, explain your thinking.
3. Is there anywhere in the city that has the same distance to all 3 stores?
4. Now a fourth store opens. Partition the city again. This time, use the applet shown below.
Attribution
illustrative mathematics. geometry. unit 1. section 9. activity 2.[br]"Who is Closest?"[br][url=https://im.kendallhunt.com/HS/teachers/2/1/9/index.html]https://im.kendallhunt.com/HS/teachers/2/1/9/index.html[br][/url]Licensed under the Creative Commons Attribution 4.0 license[br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url]
im.g.1.9.4.Another Layer (version 1)
Instructions (tessellation version 1)
[list=1][*]Imagine that each vertex (intersection) is a store from the “Who Is Closest?” activity. Repeat the process you used there to define the regions that are closest to each of the points.[/*][*]Use the Polygon Tool and the color selector in the Style Bar to enhance your design.[/*][/list]