Gr 10 Math Ch 6: The Mid Point Theorem

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?

Segment lengths and ratios. 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?

Cutting along the line joining mid points and observing the triangle. Signup and view all the answers

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

The segment DE is equal to half the length of segment BC. 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?

It is parallel to the third side. Signup and view all the answers

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

The line segment is equal to half the length of the third side. Signup and view all the answers

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

The parallelism of segments and proportions in figures. Signup and view all the answers

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

The mid-point segment is parallel to the third side and half of its length. 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?

It will bisect the third side. Signup and view all the answers

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

Determining mid-point and distances in coordinate plane problems. 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?

It is parallel to the third side and half its length. Signup and view all the answers

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

A line drawn through the mid-point of one side parallel to another side will bisect the opposite side. Signup and view all the answers

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

The third side is always equal to twice the length of the segment joining the mid-points. Signup and view all the answers

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

It identifies conditions under which line segments can be deemed parallel. Signup and view all the answers

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

Calculating mid-points and distances effectively in plane problems. Signup and view all the answers

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

The length of the segment connecting mid-points is always half that of the third side. Signup and view all the answers

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

It helps prove that certain lines are parallel in geometric figures. Signup and view all the answers

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

The parallel nature of segments created by midpoints. 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?

It will bisect the third side of the triangle. Signup and view all the answers

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

Triangles formed are necessarily similar to the original triangle. Signup and view all the answers

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

The mid-points divide the triangle into smaller but similar triangles. Signup and view all the answers

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

The lines DE and BC will coincide at a point if shifted accordingly. Signup and view all the answers