Lecture Notes: Mid Segment Theorem in Triangles

Definition of Mid Segment

• A mid segment is a line segment that connects the midpoints of two sides of a triangle.
  • If the lengths of two segments are equal, the point at which they meet is the midpoint.

Properties of the Mid Segment

• The mid segment is parallel to the third side of the triangle (base).
• The length of the mid segment is half the length of the base.
  • Example: If the base is 10 units, the mid segment is 5 units.

Additional Properties

• If you find the midpoint of another side and connect to a third midpoint, this new segment will also be a mid segment.
• All mid segments in a triangle are equal in length if they are from the same base measurements.

Example Problems

Example 1

• Given: A mid segment is 7 units.
• Conclusion: The base is double the mid segment, i.e., 14 units.

Example 2: Combining Algebra with Geometry

• Given: Mid segment identified between two midpoints.
• To find the base using the mid-segment:
  • Equation: Double the mid-segment and set it equal to the base.
  • Example Calculation:
    • Mid-segment: ( x + 4 )
    • Base: ( 3x - 6 )
    • Equation: ( 2(x + 4) = 3x - 6 )
    • Solve:
      • Distribute: ( 2x + 8 = 3x - 6 )
      • Rearrange: ( x - 6 = 8 )
      • Solution: ( x = 14 )

Conclusion

• Doubling the mid-segment gives the base length.
• Use this property to solve problems involving mid-segments and bases in triangles.

Additional Resources

• "Mario's Math Tutoring" YouTube channel for further math tutorials and resources.