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5.1 – MIDSEGMENT THEOREM

5.1 – MIDSEGMENT THEOREM. Midsegment:. Line connecting the midpoints of two sides of the triangle. The sides of a triangle are A (0, 4), B (4, 0), and C (8, 6).

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5.1 – MIDSEGMENT THEOREM

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  1. 5.1 – MIDSEGMENT THEOREM

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

  3. The sides of a triangle are A(0, 4), B(4, 0), and C(8, 6). Find the midpoint of and . Call the points D and E respectively and connect them with a line. This line is called a midsegment. (8, 6) C A (0, 4) B (4, 0)

  4. A(0, 4) C(8, 6) B(4, 0) C(8, 6) D E

  5. (4, 5) C (8, 6) D A (0, 4) E (6, 3) B (4, 0)

  6. Find the slope of and What do you notice? A(0, 4) B(4, 0) = AB = = = D(4, 5) E(6, 3) = DE = = = They are parallel

  7. Find the distance for AB and DE. What do you notice? A(0, 4) B(4, 0) D(4, 5) E(6, 3) AB is twice the length of DE

  8. 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

  9. 8

  10. 14

  11. 4

  12. 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 =

  13. 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 =

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