Download Geometry 5-4 Midsegments

Geometry 5-4 Midsegments
Midsegment of a triangle: a segment that connects the
midpoints of two sides of the triangle.
Midsegment Triangle: the triangle formed by the 3
midsegments
Midpoints: X, Y, Z
Midsegments: XY, YZ, ZX
Midsegment triangle: ΔXYZ
Midsegment Theorem
The midsegment is ½ the length of its parallel
side.
If BC = 30
DE = 15
A
BF = FC = 15
E
D
If EF = 12
AB = 24
B
F
C
AD = DB = 15
Midsegment Angles
All of the angles of the midsegment triangle are
the same as the original triangle.
A
60°
E
D
70°
50°
B
F
C
Example
• Find the perimeter and area of both the original
and midsegment triangle.
24
26
10
Example
• Solve for the value of x given DE and EF are
midsegments.
A
E
D
B
F
C