Download Triangle Inequality Theorem

ESSENTIAL QUESTION:
How to use triangle
measurements to decide
which side is longest
and which angle is largest?
Theorem 4.10

If one side of a triangle is longer than
another side, then the angle opposite the
longer side is larger than the angle
opposite the shorter side.
Example 1
Order Angle Measures
Name the angles from largest to smallest.
SOLUTION
TV > TU, so mU > mV. Also, TU > UV, so mV > mT.
ANSWER
The order of the angles from largest to
smallest is U, V, T.
Checkpoint
Order Angle Measures and Side Lengths
Name the angles from largest to smallest.
1.
3.
2.
Checkpoint
Order Angle Measures and Side Lengths
Name the angles from largest to smallest.
1.
ANSWER
N; L; M
ANSWER
Q; R; P
ANSWER
U; S; T
2.
3.
Theorem 4.11

If one angle of a triangle is larger than
another angle, then the side opposite the
larger angle is longer than the side
opposite the smaller angle.
Example 2
Order Side Lengths
Name the sides from longest to shortest.
SOLUTION
mE > mD, so DF > FE. Also, mD > mF, so FE > DE.
ANSWER
The order of the sides from longest to
shortest is DF, FE, DE.
Checkpoint
Order Angle Measures and Side Lengths
Name the sides from longest to shortest.
4.
6.
5.
Checkpoint
Order Angle Measures and Side Lengths
Name the sides from longest to shortest.
4.
ANSWER
GH; JG; JH
ANSWER
DE; EF; DF
ANSWER
AC; AB; BC
5.
6.
Triangle Inequality
Theorem

The sum of the lengths of any two sides
of a triangle is greater than the length of
the third side.
Triangle Inequality
Theorem

The sum of the lengths of any two sides
of a triangle is greater than the length of
the third side.
Example 3
Use the Triangle Inequality
Can the side lengths form a triangle? Explain.
a. 3, 5,
9
SOLUTION
a.
These lengths do
not form a
triangle, because
3 + 5 < 9.
b. 3, 5,
8
c. 3, 5,
7
b.
c.
These lengths do
not form a
triangle,
because 3 + 5 = 8.
These lengths
do form a
triangle,
because 3 + 5
> 7, 3 + 7 > 5,
and 5 + 7 > 3.
Checkpoint
Use the Triangle Inequality
Can the side lengths form a triangle? Explain.
7. 5, 7, 13
8. 6, 9, 12
9. 10, 15, 25
Checkpoint
Use the Triangle Inequality
Can the side lengths form a triangle? Explain.
7. 5, 7, 13
ANSWER
No; 5 + 7 < 13.
8. 6, 9, 12
ANSWER
Yes; 6 + 9 > 12, 6 + 12 > 9,
and 9 + 12 > 6.
9. 10, 15, 25
ANSWER
No; 10 + 15 = 25.
1. BD is a median of ∆ABC. Find the
length of AD.
ANSWER
7
2. Point P is the centroid of ∆LMN
and QN = 45. Find PN and QP.
ANSWER
PN = 30, QP = 15
3. Point D is the centroid of ∆ABC and DE = 14.
Find CD and CE.
ANSWER
CD = 28, CE = 42

Hw Practice 4.7A