QUESTION 53 If AB and CD are divided proportionally at points M and N (as shown), AB then AM CN CD D. O True False

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
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**Question 53**

If \( \overline{AB} \) and \( \overline{CD} \) are divided proportionally at points \( M \) and \( N \) (as shown), then 

\[
\frac{AB}{AM} = \frac{CN}{CD}
\]

### Diagram Explanation:

- **Line Segment \( \overline{AB} \):** 
  - Points \( A \), \( M \), and \( B \) are marked on a straight line. 
  - \( M \) divides \( \overline{AB} \) into two parts: \( \overline{AM} \) and the remainder of the segment to \( B \).

- **Line Segment \( \overline{CD} \):** 
  - Points \( C \), \( N \), and \( D \) are marked similarly on another straight line. 
  - \( N \) divides \( \overline{CD} \) into two parts: \( \overline{CN} \) and the remainder of the segment to \( D \).

### Question:

- Choose True or False for the equality \( \frac{AB}{AM} = \frac{CN}{CD} \).

### Options:
- True
- False
Transcribed Image Text:**Question 53** If \( \overline{AB} \) and \( \overline{CD} \) are divided proportionally at points \( M \) and \( N \) (as shown), then \[ \frac{AB}{AM} = \frac{CN}{CD} \] ### Diagram Explanation: - **Line Segment \( \overline{AB} \):** - Points \( A \), \( M \), and \( B \) are marked on a straight line. - \( M \) divides \( \overline{AB} \) into two parts: \( \overline{AM} \) and the remainder of the segment to \( B \). - **Line Segment \( \overline{CD} \):** - Points \( C \), \( N \), and \( D \) are marked similarly on another straight line. - \( N \) divides \( \overline{CD} \) into two parts: \( \overline{CN} \) and the remainder of the segment to \( D \). ### Question: - Choose True or False for the equality \( \frac{AB}{AM} = \frac{CN}{CD} \). ### Options: - True - False
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