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Questions and Answers
What does Thales' theorem state about a line parallel to one side of a triangle?
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?
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?
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?
If AB = AD and B1 = D1, what relationship is shown between these segments?
Which property of triangle ABC is primarily illustrated through the application of Thales' theorem in the context provided?
Which property of triangle ABC is primarily illustrated through the application of Thales' theorem in the context provided?
Flashcards
Parallel Line in a Triangle
Parallel Line in a Triangle
A line that is parallel to one side of a triangle and intersects the other two sides.
Thales' Theorem
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
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
Specific Triangle Properties
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Triangle Geometric Properties
Triangle Geometric Properties
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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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