IM Geometry Unit 1
Table of Contents
- Lesson 1
- IM G Unit 1 Lesson 1
- Lesson 2
- Lesson 3
- IM G 1.3.3
- IM G 1.3 Cool Down
- Lesson 4
- IM G 1.4.1
- IM G 1.4 Cool Down
- Lesson 5
- Copy of G.1.5.2 Make It Right
- Lesson 6
- IM G 1.6.1
- IM G 1.6 Cool Down
- Lesson 7
- Copy of G.1.7.2 It’s Cool to Be Square
- Lesson 8
- IM G 1.8 Constructions
- IM G 1.8 Cool Down
- Assessment
- IM G 1.1-1.9 Assessment
IM G Unit 1 Lesson 1
Copy this figure using only the Pen tool and no other tools.
Familiarize yourself with your digital straightedge and compass tools by drawing a few circles of different sizes, drawing a few line segments of different lengths, and extending some of those line segments in both directions.
Copy the figure by completing these steps with the Line, Segment, and Ray tools and the Circle and Compass tools: [br][list=1][*]Draw a point and label it A.[/*][*]Draw a circle centered at point A with a radius equal to length [i]PQ[/i].[/*][*]Mark a point on the circle and label it [i]B[/i].[/*][*]Draw another circle centered at point [i]B[/i] that goes through point .[i]A[/i][/*][*]Draw a line segment between points [i]A[/i] and [i]B[/i].[/*][/list]
[list=1][*]Create a circle centered at [i]A[/i] with radius [i]AB[/i].[/*][*]Estimate the midpoint of segment [i]AB[/i], mark it with the Point on Object tool, and label it [i]C[/i].[/*][*]Create a circle centered at [i]B[/i] with radius [i]BC[/i]. Mark the 2 intersection points with the Intersection tool. Label the one toward the top of the page as [i]D[/i] and the one toward the bottom as [i]E[/i].[/*][*]Use the Polygon tool to connect points [i]A, D, [/i] and [i]E[/i] to make triangle .[/*][/list]
Here is a hexagon with all congruent angles and all congruent sides (called a [i]regular[/i] hexagon). [br][list=1][*]Try to draw a copy of the regular hexagon using only the pen tool. [/*][*]Draw your copy next to the hexagon given, and then drag the given one onto yours.[/*][/list]
[list=1][*]How do you know each of the sides of the shape are the same length? Show or explain your reasoning.[/*][/list]
IM G Unit 1 Lesson 1 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/1/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
IM G 1.3.3
Use the tools available to find the perpendicular bisector of segment [i]PQ[/i] .
IM G Unit Lesson 3 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/3/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
IM G 1.4.1
What do you notice? What do you wonder?
Use the polygon tool (the one that looks like a triangle) to draw at least 2 polygons on the figure. The vertices of your polygon should be intersection points in the figure. Shade in your polygons using different colors to make them easier to see. Use the style bar to change the color. [br][br]The style bar is in the upper right corner of the applet. It has a circle and a triangle.
Write at least 2 conjectures about the polygons you made.
IM G Unit 1 Lesson 4 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/4/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
Copy of G.1.5.2 Make It Right
Here is a line [i]l [/i]with a point labeled [i]C[/i] :[br][br]Use straightedge and compass tools to construct a line perpendicular to [i]l[/i] that goes through [i]C[/i] .[br]
Here is an angle:
[list=1][*]Estimate the location of a point [i]D[/i] so that angle [i]DBC[/i] is approximately congruent to angle [i]CBD[/i] .[/*][*]Use compass and straightedge tools to create a ray that divides angle into 2 congruent angles. [/*][/list]
How close is the ray to going through your point [i]D[/i] ?
IM G Unit 1 Lesson 5 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/5/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
IM G 1.6.1
Each pair of shapes is congruent. Identify a transformation or sequence of transformations that could take one shape to the other.
Here is a line [i]m[/i] and a point C [i]not[/i] on the line. Use straightedge and compass tools to construct a line perpendicular [i]m[/i] to line that goes through point [i]C[/i].
How do you know the line you constructed is perpendicular to line [i]m[/i]?
Here is a line [i]m[/i] and a point C [i]not[/i] on the line. Use straightedge and compass tools to construct a line [b]parallel[/b] [i]m[/i] to line that goes through point [i]C[/i].
IM G Unit 1 Lesson 6 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/6/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
Copy of G.1.7.2 It’s Cool to Be Square
Use straightedge and compass tools to construct a square with segment [i]AB[/i] as one of the sides.
Here is square [i]ABCD[/i] with diagonal [i]BD[/i] drawn:[list=1][*]Construct a circle centered at [i]A[/i] with radius [i]AD[/i] .[/*][*]Construct a circle [i]C [/i]centered at with radius [i]CD[/i] .[/*][*]Draw the diagonal [i]AC[/i] and write a conjecture about the relationship between the diagonals [i]BD[/i] and [i]AC[/i] .[/*][*]Label the intersection of the diagonals as point [i]E[/i] and construct a circle centered at [i]E[/i] with radius [i]EB[/i]. [/*][/list]
Use your conjecture and straightedge and compass tools to construct a square inscribed in a circle.
IM G Unit 1 Lesson 7 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/7/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
IM G 1.8 Constructions
Here is a GeoGebra Constructions App.[br]Try all the tools in the workspace.[br][list=1][*]Find the Undo button.[br]undo[br][img]https://cms-im.s3.amazonaws.com/Ae7hHho213ZZr8BwkThJRGHF?response-content-disposition=inline%3B%20filename%3D%22G1%20undo%20copy2.png%22%3B%20filename%2A%3DUTF-8%27%27G1%2520undo%2520copy2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJFC4WL6K24MWHIRQ%2F20200824%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20200824T184624Z&X-Amz-Expires=300&X-Amz-SignedHeaders=host&X-Amz-Signature=d621773492868509d88e2303b6b7b536e5400ef69c645c140fe59592e2cabcc0[/img][img]https://im.kendallhunt.com/assets/expand-b65016df6e2186dc8daa3c8a99c2c901b21df60d53a38770bac05e01cf1887e2.png[/img] Expand Image[br][br][/*][*]Click on the image of 3 stacked segments, the Main Menu, to save your work or go to a new page.[br][/*][/list]
[list=1][*]Which tools do the same work as a straightedge?[/*][/list]
The Constructions App has 3 tools to make a point. In this applet, all 3 point tools have been used.[list=1][*]Open the Style Menu, Drag each point and each line around to see what happens in the Style Menu.[/*][*]Look at the way the points are defined in the Style Menu.[/*][/list]
There are several ways to use the compass tool. First, set up a workspace that looks something like the image:[list=1][*]Use the Constructions App below to recreate this image by following the instructions.[/*][*]Draw circle [i]A[/i] through point [i]B[/i].[/*][*]Draw segment [i]CD[/i] not intersecting the circle centered at [i]A[/i] .[/*][*]Draw point [i]E[/i] not intersecting the circle centered at [i]A[/i] or segment [i]CD.[/i] [/*][/list][br][img]https://cms-im.s3.amazonaws.com/r2uWsKBESud9VzKZS1aWjNeq?response-content-disposition=inline%3B%20filename%3D%22G1.8.1.1%20How%20Do%20Digital%20Construction%20Tools%20Work%20sm.png%22%3B%20filename%2A%3DUTF-8%27%27G1.8.1.1%2520How%2520Do%2520Digital%2520Construction%2520Tools%2520Work%2520sm.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJFC4WL6K24MWHIRQ%2F20200824%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20200824T184624Z&X-Amz-Expires=300&X-Amz-SignedHeaders=host&X-Amz-Signature=c3a999d6fb5c78ffff7f2f9eae346cce5a4e46cd24076f941f5803d8f3dfae15[/img]
[list=1][*]Select the compass tool and then click on segment [i]CD.[/i] What happens?[/*][*]Now click on the point [i]E. [/i]What happens?[/*][/list]
[list=1][*]Make a new segment [i]EF[/i] that is the same length as [i]CD[/i].[/*][*]Make a circle with the same radius as the circle [i]A[/i] centered at [i]E[/i] .[/*][/list]
IM G Unit 1 Lesson 8 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/8/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].
IM G 1.1-1.9 Assessment
Here are two circles with center [i]A.[/i]
Question 1
What do you know about line segments [i]AH, AI, AG, [/i]and [i]AF?[br][/i]Explain how you know this.
What do you know about triangles [i]AHI and AFG[br][/i]How do you know this is true?
Follow this set of instructions and then answer the question below.[br]1. Draw 2 points, [i]A [/i]and [i]B.[br][/i]2. Draw a circle centered at [i]A[/i] with radius [i]AB[/i].[br]3. Draw a circle centered at [i]B[/i] with radius [i]AB[/i].[br]4. Label the intersection points of the circles [i]C [/i]and [i]D.[br][/i]5. Draw segments [i]AC, BC, AD,[/i] and [i]BD[/i].
Question 2
What kind of quadrilateral did you construct? How do you know?
IM G Unit 1 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/9/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].