1. 
Given DE is the length
of the midsegment.
Find AB. 

Solution:
The midsegment is half of the third side.
7 is half of 14.
AB = 14. 




2. 
Given DE, DF, and FE
are the lengths of midsegments. Find the perimeter of triangle ABC.


Solution:
The midsegment is half of the third side.
6 is half of 12 so AC = 12
7 is half of 14 so CB = 14
8 is half of 16 so AB = 16
The perimeter of the large triangle ABC is:
12 + 14 + 16 = 42. 




3. 


Statements 
Reasons 
1. 

1. 
Given 
2. 

2. 
The midsegment of a triangle is
parallel to the third side of the triangle. 
3. 

3. 
If two parallel lines are cut by
a transversal, the corresponding angles are
congruent. 
4. 

4. 
Transitive property. 
5. 

5. 
The midpoint of a segment
divides the segment into two congruent segments. 
6. 

6. 
AAS. If 2 angles
and the nonincluded side of one triangle are
congruent to the corresponding parts of another
triangle, the triangles are congruent. 
