Triangle midsegment theorem

1
Triangle midsegment theorem

• A midsegment of a triangle is a segment that
  joins the midpoints of 2 sides of the triangle
• Every triangle has 3 midsegments

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Theorem 55-1Triangle Midsegment Theorem

• The segment joining the midpoints of 2 sides of a
  triangle is parallel to, and half the length of
  the third side

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Find the values of k and y

• ED is the midsegment of tri ABC

5
7
y
4
Theorem 55-2

• If a line is parallel to one side of a triangle
  and it contains the midpoint of another side,
  then it passes through the midpoint of the third
  side

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Identifying midpoints of sides of a triangle

• Triangle MNP has vertices M(-2,4), N(6,2), and
  P(2,-1). QR is a midsegment of tri MNP. Find the
  coordinates of Q and R
• 1. graph points
• 2. find midpoints of MN and NP using midpoint
  formula
• 3.Q (4, 1/2)
• R (2,3)

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Midsegment triangle

• A midsegment triangle is the triangle formed by
  the 3 midsegments of a triangle.
• Midsegment triangles are similar to the original
  triangle and to the triangles formed by each
  midsegment - ABC, EFD, ADF, DBE, FEC are similar

B
D
E
C
A
F
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Applying similarity

• Show that Tri STU is similar to tri PQR
• ST 1/2 PR,SU 1/2 QR, TU 1/2 QP, so tri STU
  is similar to tri PQR by SSS similarity .
• Find PQ

Q
2x7
T
S
4x-3
19
R
P
U
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Practice

• DE is a midsegment of tri ABC. Find the values of
  x and y

8
12
y
x
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Practice

• Triangle FGH has vertices at F(-2,4), G(6,2) and
  H(2, -1). DE is a midsegment of tri FGH. Find the
  coordinates of D and E

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Find the perimeter of the midsegment triangle

• Find perimeter of tri EDF

5
14
3x2
2x4
11
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