Gr 10 Math Ch 6: The Mid Point Theorem
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Questions and Answers

What does the Mid-Point Theorem state about the relationship between the segment joining the mid-points of two sides of a triangle and the third side?

  • The segment is parallel to the third side and equal to the length of the third side.
  • The segment is orthogonal to the third side and equal to half the length of it.
  • The segment is always shorter than the third side by a fixed ratio.
  • The segment is parallel to the third side and equal to half the length of the third side. (correct)

What conclusion can be drawn from the converse of the Mid-Point Theorem?

  • A line segment drawn parallel to one side will always bisect two other sides.
  • If a line is drawn through the mid-point of a side parallel to a second side, it will bisect the opposite vertex.
  • A line drawn through the mid-point of one side that is parallel to another side will bisect the third side. (correct)
  • The mid-point of any triangle side can be used to find the centroid of the triangle.

In the context of the Mid-Point Theorem, what geometric considerations does the line segment joining mid-points create?

  • It establishes parallel lines and proportionate segments. (correct)
  • It creates an acute triangle.
  • It forms two isosceles triangles.
  • It ensures all angles in the triangle remain equal.

Which application of the Mid-Point Theorem is primarily beneficial in proving similarity in triangles?

<p>Segment lengths and ratios. (D)</p> Signup and view all the answers

When conducting an investigation as per the Mid-Point Theorem, which action specifically highlights the relationships between triangle segments?

<p>Cutting along the line joining mid points and observing the triangle. (A)</p> Signup and view all the answers

What key observation can be made about the lengths of the segments in the Mid-Point Theorem?

<p>The segment DE is equal to half the length of segment BC. (D)</p> Signup and view all the answers

What is the relationship between the line segment joining the mid-points of two sides of a triangle and the third side?

<p>It is parallel to the third side. (C)</p> Signup and view all the answers

Which of the following statements about the Mid-Point Theorem is true?

<p>The line segment is equal to half the length of the third side. (B)</p> Signup and view all the answers

In an application of the Mid-Point Theorem, what is primarily proven using this theorem?

<p>The parallelism of segments and proportions in figures. (C)</p> Signup and view all the answers

What would be a valid conjecture based on the mid-points and the line segment joining them?

<p>The mid-point segment is parallel to the third side and half of its length. (C)</p> Signup and view all the answers

What is the result of drawing a line through the mid-point of one side of a triangle parallel to another side?

<p>It will bisect the third side. (A)</p> Signup and view all the answers

In the context of coordinate geometry, what important role does the Mid-Point Theorem play?

<p>Determining mid-point and distances in coordinate plane problems. (C)</p> Signup and view all the answers

What geometric property does the Mid-Point Theorem guarantee about the line segment connecting the mid-points of two sides of a triangle?

<p>It is parallel to the third side and half its length. (C)</p> Signup and view all the answers

Which statement accurately reflects the result of applying the converse of the Mid-Point Theorem?

<p>A line drawn through the mid-point of one side parallel to another side will bisect the opposite side. (C)</p> Signup and view all the answers

In an investigation using the Mid-Point Theorem, what significant observation can be made about triangle segments?

<p>The third side is always equal to twice the length of the segment joining the mid-points. (A)</p> Signup and view all the answers

How does the Mid-Point Theorem support geometric proofs concerning parallel lines?

<p>It identifies conditions under which line segments can be deemed parallel. (D)</p> Signup and view all the answers

Which application of the Mid-Point Theorem is most closely associated with coordinate geometry?

<p>Calculating mid-points and distances effectively in plane problems. (C)</p> Signup and view all the answers

What conclusion can be drawn about the lengths of segments in the context of the Mid-Point Theorem?

<p>The length of the segment connecting mid-points is always half that of the third side. (D)</p> Signup and view all the answers

What is a direct consequence of applying the Mid-Point Theorem in calculating segment proportions?

<p>It helps prove that certain lines are parallel in geometric figures. (D)</p> Signup and view all the answers

Which aspect of the Mid-Point Theorem is involved in constructing geometric proofs?

<p>The parallel nature of segments created by midpoints. (B)</p> Signup and view all the answers

If a line is drawn through the mid-point of one side of a triangle and is parallel to the second side, what geometric result is guaranteed?

<p>It will bisect the third side of the triangle. (D)</p> Signup and view all the answers

In the context of similarity and the Mid-Point Theorem, what statement holds true regarding triangles?

<p>Triangles formed are necessarily similar to the original triangle. (C)</p> Signup and view all the answers

Which of the following statements about the Mid-Point Theorem is false when applied to a scalene triangle?

<p>The mid-points divide the triangle into smaller but similar triangles. (A)</p> Signup and view all the answers

What conjecture can be made after shifting triangle ADE to place vertex D on vertex B?

<p>The lines DE and BC will coincide at a point if shifted accordingly. (D)</p> Signup and view all the answers

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