Thales Theorem in a Triangle

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Questions and Answers

What does Thales' theorem state about a line parallel to one side of a triangle?

  • It divides the sides into equal segments.
  • It creates two similar triangles.
  • It is always perpendicular to the base.
  • It divides the two sides proportionally. (correct)

In the given properties, if AM/MB = AN/NC, what can be inferred about the segments?

  • The segments are proportional. (correct)
  • MN is equal in length to BC.
  • The segments are not related at all.
  • MN is a median of the triangle.

What role does the line MN play in relation to triangle ABC?

  • It serves as a base of triangle ABC.
  • It acts as a height of the triangle.
  • It intersects the triangle at an angle.
  • It is parallel to BC. (correct)

If AB = AD and B1 = D1, what relationship is shown between these segments?

<p>They are all equal in length. (D)</p> Signup and view all the answers

Which property of triangle ABC is primarily illustrated through the application of Thales' theorem in the context provided?

<p>The lengths of segments are directly proportional. (A)</p> Signup and view all the answers

Flashcards

Parallel Line in a Triangle

A line that is parallel to one side of a triangle and intersects the other two sides.

Thales' Theorem

A theorem stating that if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Ratio of Segments

The ratio of the length of a segment from a vertex to a point on a side of a triangle, to the length of the remaining segment on that side.

Specific Triangle Properties

Relates to a specific triangle and the properties of its segments caused by a parallel line.

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Triangle Geometric Properties

A set of rules or relationships that apply to triangles.

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Study Notes

Thales Theorem in a Triangle

  • If a line parallel to one side of a triangle is drawn intersecting the other two sides, then it divides the two sides proportionally.
  • In the given triangle ABC, MN is parallel to BC, intersecting sides AB and AC at points M and N respectively
  • This implies that AM/MB = AN/NC
  • Further, AM/AB = AN/AC = MN/BC.

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