Transcript 5.3 Theorems Involving Parallel Lines

• Midsegment of a Triangle –
-The segment connecting the midpoints of two
sides of the triangle.
Theorem
• The segment that joins the midpoints of two sides of
a triangle.
(1) is parallel to the third side.
(2) is half as long as the third side.
C
D
A
E
B
Some Examples
M, N, and T are midpoints
Z
If XZ = 10, then MN = _____
If TN = 7, then XY = _____
N
T
If ZN = 8, then TM = _____
If XY = k, then TN = _____
Suppose XY =10, YZ =14, and
XZ= 8, find the lengths of the
sides of triangle MNT.
X
M
Y
A
12
8
D
E
12
B
F
10
C
Assuming that D, E, and F are midpoints, find all
segment lengths.
A
D
E
2x+16
B
8x-12
C
Find x, y, and z, and each segment length.