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Prove that if PR is not parallel to BC then # figure 1.13 AP |AR| |AB| |AC| . |AP| If P is any point on AB and Q is any point on AC then PQ is paraellel to BC if and only if 1.13* |AB| |AQ| = *figure |AC|

Prove that if PR is not parallel to BC then # figure 1.13 AP |AR| |AB| |AC| . |AP| If P is any point on AB and Q is any point on AC then PQ is paraellel to BC if and only if 1.13* |AB| |AQ| = *figure |AC|

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Prove that if PR is not parallel to BC, then \(\frac{|AP|}{|AB|} \neq \frac{|AR|}{|AC|}\) (Figure 1.13).** If P is any point on AB and Q is any point on AC, then PQ is parallel to BC *if and only if* \(\frac{|AP|}{|AB|} = \frac{|AQ|}{|AC|}\). *(Figure 1.13)* (Note: The text contains a typographical error, "paraellel" should be "parallel.")
Transcribed Image Text:**Prove that if PR is not parallel to BC, then \(\frac{|AP|}{|AB|} \neq \frac{|AR|}{|AC|}\) (Figure 1.13).** If P is any point on AB and Q is any point on AC, then PQ is parallel to BC *if and only if* \(\frac{|AP|}{|AB|} = \frac{|AQ|}{|AC|}\). *(Figure 1.13)* (Note: The text contains a typographical error, "paraellel" should be "parallel.")
The image is a diagram illustrating the "Converse of the Thales Theorem," labeled as Figure 1.13. ### Diagram Details: - **Triangle **: The diagram shows triangle \( ABC \). - **Points and Lines**: - A line \( \ell \) extends across the diagram with points labeled \( P \) and \( Q \) on it. - Point \( A \) is the vertex of the triangle opposite the base \( BC \). - Two segments, \( AP \) and \( AQ \), originate from point \( A \) extending downwards intersecting line \( \ell \) at \( P \) and \( Q \). - Another segment \( PR \) extends from \( P \) and intersects the triangle at point \( R \) on side \( AC \). This diagram is typically used to demonstrate the converse of the Thales Theorem, which pertains to the properties of a line parallel to one side of the triangle and its intersections with the other two sides.
Transcribed Image Text:The image is a diagram illustrating the "Converse of the Thales Theorem," labeled as Figure 1.13. ### Diagram Details: - **Triangle **: The diagram shows triangle \( ABC \). - **Points and Lines**: - A line \( \ell \) extends across the diagram with points labeled \( P \) and \( Q \) on it. - Point \( A \) is the vertex of the triangle opposite the base \( BC \). - Two segments, \( AP \) and \( AQ \), originate from point \( A \) extending downwards intersecting line \( \ell \) at \( P \) and \( Q \). - Another segment \( PR \) extends from \( P \) and intersects the triangle at point \( R \) on side \( AC \). This diagram is typically used to demonstrate the converse of the Thales Theorem, which pertains to the properties of a line parallel to one side of the triangle and its intersections with the other two sides.
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