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BC D ++ H 0 10 Students in a geometry class were instructed to place markers along a number line to represent points A, B, C, D, and E. They were then asked to exar the points and compare them to segment AC. Which of the following statements made by students in the class is true? AB is congruent to AC because AC contains AB. B CD is congruent to AC because both segments share an endpoint. с DE is congruent to AC because both segments have the same length. D AC is congruent to CE because the length of CE is twice the length of AC

BC D ++ H 0 10 Students in a geometry class were instructed to place markers along a number line to represent points A, B, C, D, and E. They were then asked to exar the points and compare them to segment AC. Which of the following statements made by students in the class is true? AB is congruent to AC because AC contains AB. B CD is congruent to AC because both segments share an endpoint. с DE is congruent to AC because both segments have the same length. D AC is congruent to CE because the length of CE is twice the length of AC

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** Students in a geometry class were instructed to place markers along a number line to represent points \( A \), \( B \), \( C \), \( D \), and \( E \). They were then asked to examine the line segments that can be constructed between any two of the points and compare them to segment \( AC \). Which of the following statements made by students in the class is true? **Diagram Explanation:** A number line is depicted with points marked at positions: \(A\) at 0, \(B\) at 2, \(C\) at 5, \(D\) at 7, and \(E\) at 10. The line is graduated in increments of 1 from 0 to 10. **Options:** A. \( \overline{AB} \) is congruent to \( \overline{AC} \) because \( \overline{AC} \) contains \( \overline{AB} \). B. \( \overline{CD} \) is congruent to \( \overline{AC} \) because both segments share an endpoint. C. \( \overline{DE} \) is congruent to \( \overline{AC} \) because both segments have the same length. D. \( \overline{AC} \) is congruent to \( \overline{CE} \) because the length of \( \overline{CE} \) is twice the length of \( \overline{AC} \). **Answer:** The true statement is **C**. \( \overline{DE} \) is congruent to \( \overline{AC} \) because both segments have the same length. **Explanation:** - \(\overline{AB} = 2 - 0 = 2\) - \(\overline{AC} = 5 - 0 = 5\) - \(\overline{CD} = 7 - 5 = 2\) - \(\overline{DE} = 10 - 7 = 3\) - \(\overline{CE} = 10 - 5 = 5\) From these calculations, we see that: - \(\overline{AC} = \overline{CE} = 5\), which confirms Option C is true because the length
Transcribed Image Text:**Question:** Students in a geometry class were instructed to place markers along a number line to represent points \( A \), \( B \), \( C \), \( D \), and \( E \). They were then asked to examine the line segments that can be constructed between any two of the points and compare them to segment \( AC \). Which of the following statements made by students in the class is true? **Diagram Explanation:** A number line is depicted with points marked at positions: \(A\) at 0, \(B\) at 2, \(C\) at 5, \(D\) at 7, and \(E\) at 10. The line is graduated in increments of 1 from 0 to 10. **Options:** A. \( \overline{AB} \) is congruent to \( \overline{AC} \) because \( \overline{AC} \) contains \( \overline{AB} \). B. \( \overline{CD} \) is congruent to \( \overline{AC} \) because both segments share an endpoint. C. \( \overline{DE} \) is congruent to \( \overline{AC} \) because both segments have the same length. D. \( \overline{AC} \) is congruent to \( \overline{CE} \) because the length of \( \overline{CE} \) is twice the length of \( \overline{AC} \). **Answer:** The true statement is **C**. \( \overline{DE} \) is congruent to \( \overline{AC} \) because both segments have the same length. **Explanation:** - \(\overline{AB} = 2 - 0 = 2\) - \(\overline{AC} = 5 - 0 = 5\) - \(\overline{CD} = 7 - 5 = 2\) - \(\overline{DE} = 10 - 7 = 3\) - \(\overline{CE} = 10 - 5 = 5\) From these calculations, we see that: - \(\overline{AC} = \overline{CE} = 5\), which confirms Option C is true because the length
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