The mid-segment of a triangle (also called a
midline) is a segment joining the midpoints of two sides of a
triangle.
Properties:
1.
The
mid-segment of a triangle joins the midpoints of two
sides of a triangle such that it is parallel to the third
side of the triangle.
2.
The
mid-segment of a triangle joins the midpoints of two sides
of a triangle such that its length is half the length of the third
side of the triangle.
Examples:
1.
Given DE is the length
of the mid-segment.
Find AB.
Solution:
The mid-segment is half of the third side.
7 is half of 14. AB = 14.
2.
Given DE, DF, and FE
are the lengths of mid-segments. Find the perimeter of triangle ABC.
Solution:
The mid-segment 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 mid-segment 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 non-included side of one triangle are
congruent to the corresponding parts of another
triangle, the triangles are congruent.
