Transformations and triangle congruence

Brandy Maynard, Nov 28, 2015

Table of Contents

  1. using transformation tools
    1. learning how to reflect
    2. Learning how to Translate
    3. Learn how to use Rotation
  2. Create a ray given two points
    1. Draw a Ray
  3. Congruent Triangles part 1.1
    1. Proving Triangles Congruent, Part 1
    2. Investigation 1.1
  4. Congruent Triangles part 1.2
    1. Transformation

1.

using transformation tools

This is a prerequisite lesson

  • 1. learning how to reflect
  • 2. Learning how to Translate
  • 3. Learn how to use Rotation

1.1.

learning how to reflect

Follow the directions to learn reflection
1. First we must draw a line that the image will reflect across.[br] A. select the menu item [b][i][u]line[/u][/i][/b] (it is the 3rd menu item)[icon]/images/ggb/toolbar/mode_join.png[/icon][br] B. pick a point to start with, I suggest (1,6)[br] C. pick a second point to fix the line in place. I suggest ( 2,1)[br] [br]2. Now.. select the menu item [b][i][u]reflect about a line[/u][/i][/b]. ( in menu box 9 after angles)[icon]/images/ggb/toolbar/mode_mirroratline.png[/icon][br]3. Select Triangle ABC (Click in the center of the triangle, you will see the sides bold when it is selected)[br][br]4. Select the line you drew. (You will see the line bold when it is selected)[br][br]FYI ** If at any point you feel you need to start over, click on the reset icon in the upper right hand corner of the graph.
Answer the following questions.
1. Were you able to draw the line?[br]2. Were you able to reflect the triangle?[br]3. Did the triangle reflect into the location you expected it to? Explain.
– Jennifer Silverman, Brandy Maynard

1.2.

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1.3.

–

2.

Create a ray given two points

Prerequisite skill

  • 1. Draw a Ray

2.1.

Draw a Ray

Follow the directions to draw a ray
1. Select the line/segment/ray icon [icon]/images/ggb/toolbar/mode_join.png[/icon] Select Ray.[br]2. Select the starting point A to start the drawing, and then select the lighter blue dot labeled B to fix the ray into this particular place.[br]3. Draw a second ray from A through C.
Answer the following questions
1. Were you able to find the Ray icon?[br]2. Were you able to create a ray from A through B?[br]3. Were you able to create a ray from A through C?
– Brandy Maynard

3.

Congruent Triangles part 1.1

Exploring ASA

  • 1. Proving Triangles Congruent, Part 1
  • 2. Investigation 1.1

3.1.

Proving Triangles Congruent, Part 1

[b]Use the[i] [b]Draw Ray[/b][/i] tool to complete the triangle. [/b] - 1st select the ray tool. (find it in the third menu box) - 2nd click the colored point at the vertex E of the new drawing. - 3rd click the lighter colored follow up colinear point to be sure your ray is straight and on the given picture. - 4th click the point at the other vertex D of the new drawing. - last click the lighter colored follow up colinear point to be sure your ray is straight and on the given picture. 2. You have created a new triangle in step 1. Sketch the new triangle on the grid on your worksheet.
– Jennifer Silverman, Brandy Maynard

3.2.

–

4.

Congruent Triangles part 1.2

  • 1. Transformation

4.1.

Transformation

Use one of the transformation tools to map the original triangle onto the new triangle.
1. What transformation did you use?[br]2. Can you write a mapping rule to describe your transformation formally?[br]3. Can we conclude that we have two congruent triangles here?[br]4. Can we conclude that we will always end up with congruent triangles when I start with these particular matching parts?[br]5. What were the particular matching parts we started with?
– Brandy Maynard, Jennifer Silverman

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