Lesson 2.2.4: Dilating angles
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For this lesson there are 9 steps for you to take. Scroll down and do each step one-by-one. The instructions under each step will help clarify exactly what you need to do, so please read all the instructions.
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Here is the Lesson 2.2.4 Worksheet
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1.) Start Notes: Targets
Title your notes and write the targets listed below.
Title your notes and write the targets listed below.
- I can dilate angles and polygons.
- I can prove that dilations map angles onto angles with equal measure.
2.) Notes: Warm Up
Before we dive into this lesson, I want you to make some predictions. The big question for this lesson is "How do dilations map triangles, rectangles, and other polygons?" I want you to consider this question now and write your predictions in your notes.
Answer the following questions in your notes. If you don't know the answer, make your best guess.
Before we dive into this lesson, I want you to make some predictions. The big question for this lesson is "How do dilations map triangles, rectangles, and other polygons?" I want you to consider this question now and write your predictions in your notes.
Answer the following questions in your notes. If you don't know the answer, make your best guess.
- When you dilate a triangle, what shape does it map onto?
- When you dilate a triangle, what is true about the corresponding angle measures?
- When you dilate a triangle, what is true about the corresponding sides?
- Answer the above 3 questions for rectangles and other polygons as well.
3.) Video: Targets and Warm Up
Watch this video to see what my answers are to the questions from the warm up. |
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4.) Notes: Triangle
Let's test out what actually happens when we dilate a triangle so we can verify our answers to the questions in the warm up.
Follow these steps for this activity:
Let's test out what actually happens when we dilate a triangle so we can verify our answers to the questions in the warm up.
Follow these steps for this activity:
- Get a graphing piece of paper. (If you don't know where they are, ask Mr. Eoff)
- Make a coordinate plane by drawing an x-axis and a y-axis. You will only need Quadrant 1. Make sure your x-axis goes to at least 15 and your y-axis goes to at least 11.
- Plot three points for Triangle ABC. Here are the points you should use: A(3, 1), B(7, 1), C(3, 5). Now connect your points to create the triangle.
- Plot point O at the origin (0, 0). This will be your center of dilation.
- Dilate Triangle ABC with a scale factor of r = 2.
- Compare the corresponding angles. Are they equal in measure? Write your answer in your notes.
- Compare the corresponding sides. Are they proportional? Write your answer in your notes.
5.) Video: Triangle
Watch this video to see how I followed the directions from part 4 and what my findings were. |
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6.) Notes: Proving Angles are Congruent
We want to be able to answer the question, "Why do dilations map angles onto angles of equal measure?" In order to do so, we will use the picture to the right. The image to the right shows a dilation of an angle with a scale factor or r = 2. Without measuring the angles, can you think of a way to prove the two angles are congruent (equal in measure)? Copy this dilation into your notes and then try to prove the angles are congruent. You do not need to use two column proof. If you want a hint, you proved the same thing back in Lesson 1.2.5. Click here for a link to the Exit Ticket of Lesson 1.2.5 to remind yourself what you did. |
7.) Video: Proving Angles are Congruent
Watch this video to see how I proved corresponding angles are congruent. |
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8.) Video: Lesson Summary
Watch this video and copy the notes. This is the summary of the lesson. |
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9.) Exit Ticket
Follow the directions below. You can use the image to the right to help guide you through the steps. Your quadrilateral does not have to be a parallelogram:
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