5-4/5-5 The Triangle Midsegment Theorem and
Inequalities in One Δ
A midsegment of a ∆ is a segment that joins the midpoints of two sides
of the triangle. 3 midsegments form the midsegment ∆.
Q
midsegments:
X
Y
midsegment ∆:
P
Z
R
Examples: Find x.
8x + 10
x
38
15
x
5x
Example: Find the following.
a) BD
b) m CBD
Example: Find the following.
a) JL
b) PM
c) m MLK
Example: ∆KLM is the midsegment ∆of ∆GHJ. What is the perimeter of
∆GHJ?
12
G
K
H
7
L
M
J
11
Example: Write the angles in order from smallest to largest.
G
17.2
F
19.6
20.4
________
________
________
H
Example: Write the sides in order from shortest to longest.
Q
72°
________
60°
P
________
________
K
A triangle is formed by three segments, but not every set of three
segments can form a triangle.
Example: Tell whether a ∆ can have sides with the given lengths.
a. 3, 4, 5 ________
b. 7, 10, 14 ________
c. 5, 8, 13 ________
Example: The length of 2 sides of a ∆ are 8 in and 13 in. Find the range
of possible lengths for the 3rd side.
________ < x < ________

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