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Peyton stated that she thought that the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn't always exactly 180°. Why do you think this happened? What might you say to Peyton? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial 10pt

Peyton stated that she thought that the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn't always exactly 180°. Why do you think this happened? What might you say to Peyton? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial 10pt

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Investigation into the Sum of Interior Angles in Triangles **Question:** Peyton stated that she thought the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn’t always exactly 180°. Why do you think this happened? What might you say to Peyton? **Answer:** The sum of the measures of interior angles in any triangle is indeed always 180°. If Peyton found that the sum of angles in some of her triangles did not equal 180°, this could be due to a few possible reasons: 1. **Measurement Error:** Using a protractor to measure angles can result in slight inaccuracies. Even small errors of one or two degrees for each measured angle can lead to a total that isn’t exactly 180°. 2. **Tool Precision:** The precision of the protractor could be a factor. If the protractor is not marked accurately, the measurements taken will not be exact. 3. **Drawing Accuracy:** If the triangles drawn aren’t perfect (e.g., lines aren’t exactly straight, points aren’t exactly at the intended locations), the angles measured may deviate from their true values. 4. **User Technique:** Differences in the way the protractor is used, such as not aligning it exactly with the sides of the triangle or not reading the scale correctly, can cause measurement discrepancies. **What to Say to Peyton:** I would explain to Peyton that while the mathematical principle states that the sum of the interior angles in a triangle is always 180°, practical measurements can introduce some errors. These errors can come from measurement tools, drawing inaccuracies, or slight mistakes in reading the protractor. I would encourage her to try measuring again with a focus on precision or consider averaging multiple sets of measurements to reduce the impact of any single error. **Related Visual Explanation Tools:** *The image displayed above includes an interactive toolbar from a word processor which allows for formatting and editing text. Peyton can use these tools to document her findings and observations systematically:* - **B (Bold), I (Italic), U (Underline):** To highlight important points, such as the statement and the mathematical principle. - **Paragraph Formatting Options:** For organizing her document into readable sections. - **Insert Table/Chart:** To record and compare her measurements and observations in a structured manner. - **Insert Equation:** To denote mathematical principles clearly.
Transcribed Image Text:### Investigation into the Sum of Interior Angles in Triangles **Question:** Peyton stated that she thought the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn’t always exactly 180°. Why do you think this happened? What might you say to Peyton? **Answer:** The sum of the measures of interior angles in any triangle is indeed always 180°. If Peyton found that the sum of angles in some of her triangles did not equal 180°, this could be due to a few possible reasons: 1. **Measurement Error:** Using a protractor to measure angles can result in slight inaccuracies. Even small errors of one or two degrees for each measured angle can lead to a total that isn’t exactly 180°. 2. **Tool Precision:** The precision of the protractor could be a factor. If the protractor is not marked accurately, the measurements taken will not be exact. 3. **Drawing Accuracy:** If the triangles drawn aren’t perfect (e.g., lines aren’t exactly straight, points aren’t exactly at the intended locations), the angles measured may deviate from their true values. 4. **User Technique:** Differences in the way the protractor is used, such as not aligning it exactly with the sides of the triangle or not reading the scale correctly, can cause measurement discrepancies. **What to Say to Peyton:** I would explain to Peyton that while the mathematical principle states that the sum of the interior angles in a triangle is always 180°, practical measurements can introduce some errors. These errors can come from measurement tools, drawing inaccuracies, or slight mistakes in reading the protractor. I would encourage her to try measuring again with a focus on precision or consider averaging multiple sets of measurements to reduce the impact of any single error. **Related Visual Explanation Tools:** *The image displayed above includes an interactive toolbar from a word processor which allows for formatting and editing text. Peyton can use these tools to document her findings and observations systematically:* - **B (Bold), I (Italic), U (Underline):** To highlight important points, such as the statement and the mathematical principle. - **Paragraph Formatting Options:** For organizing her document into readable sections. - **Insert Table/Chart:** To record and compare her measurements and observations in a structured manner. - **Insert Equation:** To denote mathematical principles clearly.
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