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Understanding the Midsegment Theorem in Triangles

The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. This theorem is crucial for solving various geometric problems involving triangles. For instance, given two segments, UW = 4x - 1 and YZ = 5x + 4, we can determine their lengths using algebraic methods. By applying the theorem's properties, we can find relationships between the sides of the triangle and solve for unknown variables effectively.

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Understanding the Midsegment Theorem in Triangles

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  1. 5.1 – MIDSEGMENT THEOREM

  2. Midsegment: Line connecting the midpoints of two sides of the triangle

  3. Midsegment Theorem: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as that side. x 2x

  4. 8

  5. 14

  6. 4

  7. If UW= 4x – 1 and YZ = 5x + 4, find UW and YZ. 2(4x – 1) 5x + 4 = 5x + 4 5x + 4 = 8x – 2 4 = 3x – 2 6 = 3x 4x – 1 2 = x 4(2)-1 = 7 UW = 5(2)+4 = 14 YZ =

  8. If YX= 8x – 2 and VW = 2x + 11, find YX and VW. 2(2x + 11) 8x – 2 = 8x – 2 = 4x + 22 4x – 2 = 22 8x – 2 4x = 24 2x + 11 x = 6 2(6)+11 = 23 VW = 46 8(6)-2 = YX =

  9. HW Problems #26 7z - 1 7z - 1 = 2(4z – 3) 4z - 3 7z - 1 = 8z – 6 -1 = z – 6 5 = z 7(5)-1 = 34 GH =

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