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  8-5 Proportions in Triangles
  
  8-5 Proportions in Triangles - proportional d d c b b a = a...
  
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  Proportions in Triangles Section 8-5
  
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  Thm. 8.5 Side-Splitter Thm. If a line is parallel to one side of a triangle and intersects the other 2 sides, then it divides those sides proportionally.
  b a y x = x y a b b a y x =
  
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  6.6 Triangle Midsegment Theorem A midsegment of a triangle is parallel to one side of the triangle, and its length is 1/2 the length of that side.
  A B C D AB = ½ CD
  
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  Corollary 7-1 and 7-2 If 3 or more parallel lines intersect 2 transversals, then the segments intercepted on the transversals are
  
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  Unformatted text preview: proportional. d d c b b a + = + a b c d d c b a = Thm. 8-5 Triangle-Angle-Bisector Theorem • If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. A B C r x w k k w x r = Joke Time How would you describe a frog with a broken leg? Unhoppy What did the horse say when he got to the bottom of his nose bag? That’s the last straw!...
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explanation: The provided text extract appears to be a set of notes or slides on the topic of proportions in triangles, which is a concept in geometry. It includes several theorems and corollaries, such as the Side-Splitter Theorem, Triangle Midsegment Theorem, and Triangle-Angle-Bisector Theorem, along with their respective mathematical expressions. The text does not contain a specific question or a question and answer. It is more of an educational resource or lecture material.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: {[ promptMessage ]}
  
  Bookmark it
  
  {[ promptMessage ]}
  
  8-5 Proportions in Triangles
  
  8-5 Proportions in Triangles - proportional d d c b b a = a...
  
  This preview shows pages 1–11. Sign up to view the full content.
  
  Proportions in Triangles Section 8-5
  
  This preview has intentionally blurred sections. Sign up to view the full version.
  
  View Full Document
  Thm. 8.5 Side-Splitter Thm. If a line is parallel to one side of a triangle and intersects the other 2 sides, then it divides those sides proportionally.
  b a y x = x y a b b a y x =
  
  This preview has intentionally blurred sections. Sign up to view the full version.
  
  View Full Document
  6.6 Triangle Midsegment Theorem A midsegment of a triangle is parallel to one side of the triangle, and its length is 1/2 the length of that side.
  A B C D AB = ½ CD
  
  This preview has intentionally blurred sections. Sign up to view the full version.
  
  View Full Document
  Corollary 7-1 and 7-2 If 3 or more parallel lines intersect 2 transversals, then the segments intercepted on the transversals are
  
  This preview has intentionally blurred sections. Sign up to view the full version.
  
  View Full Document
  
  This preview has intentionally blurred sections. Sign up to view the full version.
  
  View Full Document
  This is the end of the preview. Sign up to access the rest of the document.
  
  Unformatted text preview: proportional. d d c b b a + = + a b c d d c b a = Thm. 8-5 Triangle-Angle-Bisector Theorem • If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. A B C r x w k k w x r = Joke Time How would you describe a frog with a broken leg? Unhoppy What did the horse say when he got to the bottom of his nose bag? That’s the last straw!...
  View Full Document
  
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  8-5 Proportions in Triangles - proportional d d c b b a = a...
  
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text extract appears to be a set of notes or slides on the topic of proportions in triangles, which is a concept in geometry. It includes several theorems and corollaries, such as the Side-Splitter Theorem, Triangle Midsegment Theorem, and Triangle-Angle-Bisector Theorem, along with their respective mathematical expressions. The text does not contain a specific question or a question and answer. It is more of an educational resource or lecture material.
  
  Label: no-question