anonymous
  • anonymous
Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures
Geometry
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anonymous
  • anonymous
Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures
Geometry
chestercat
  • chestercat
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anonymous
  • anonymous
I have no clue :(
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
Given triangle ABC with segment DE parallel to side B.

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mathstudent55
  • mathstudent55
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anonymous
  • anonymous
I don't get why the numbers are there if we just need to prove that the two sides are proportional @mathstudent55
mathstudent55
  • mathstudent55
Using corresponding angles and the parallel lines, angles 1 and 2 are congruent. Also, angles 3 and4 are congruent. By AA Similarity, triangles ABC and ADE are similar. That makes the lengths of corresponding sides proportional. \(\dfrac{AD}{AB} = \dfrac{AE}{AC} \) By the segment addition postulate, we can rewrite segments AB and AC as sums: \(\dfrac{AD}{AD + DB} = \dfrac{AE}{AE + EC} \)
mathstudent55
  • mathstudent55
I numbered the angles to make it easier to mention them instead of using three-letter names. Angle 1 is easier to write than angle ADE.
anonymous
  • anonymous
ohh ok I see
mathstudent55
  • mathstudent55
We can now take the reciprocal of both sides: \(\dfrac{AD + DB}{AD} = \dfrac{AE + EC}{AE} \) By a property of proportions, we can conclude: \(\dfrac{DB}{AD} = \dfrac{EC}{AE} \)
mathstudent55
  • mathstudent55
That proves it.
anonymous
  • anonymous
thank you so much .. understand it a lot better now :)
mathstudent55
  • mathstudent55
You are welcome.

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