Transcript Triangle midsegment theorem A Every triangle has 3 midsegments

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
Theorem 55-1
Triangle Midsegment Theorem
• The segment joining the midpoints of 2
sides of a triangle is parallel to, and half
the length of the third side
Find the values of k and y
• ED is the midsegment of tri ABC
5
7
y
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
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)
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
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
2x+7
T
S
4x-3
19
P
R
U
Practice
• DE is a midsegment of tri ABC. Find
the values of x and y
8
12
y
x
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
Find the perimeter of the midsegment
triangle
• Find perimeter of tri EDF
5
14
2x+4
3x+2