math 8 triangle inequalities

1. LESSON 5-5
INEQUALITIES IN TRIANGLES
OBJECTIVE:
To use inequalities involving angles
and sides of triangles

2. Theorem 5-10
If a triangle is scalene, then the largest angle
lies opposite the longest side
and the smallest angle
lies opposite the shortest side.
17”
X
Y
Z
29”
32”
Example 1: List the angles
from smallest to largest
∠Z ∠Y ∠X

3. Theorem 5-11(Converse of Theorem 5-10)
If a triangle is scalene, then the longest side
lies opposite the largest angle,
and the shortest side
lies opposite the smallest angle.
R
Q
S
30°
Example 2: In ∆QRS, list
the sides from
smallest to largest
SR QS QR

4. Example 3:
In ∆TUV, which side is the shortest?
58°
U
V
62°
Use ∆ sum to find m∠T.
m∠T = 60°, so ∠U is smallest
Therefore VT is shortest
T

5. Theorem 5-12 The Triangle Inequality Theorem
The sum of the lengths of any two sides of a
triangle is
greater than the length of the third side.

6. Example 4:
Can a triangle have sides with the given lengths?
Explain.
a) 3ft., 7ft., 8ft. b) 3cm., 6cm., 10cm.
Yes, 3 + 7 > 8 NO, 3 + 6 < 10

7. Example 5:
A triangle has sides of lengths 8cm and 10cm.
Describe the lengths possible for the third side.
Let x = the length of the 3rd side.
The sum of any 2 sides must be
greater than the 3rd.

8. x + 8 > 10
x > 2
x + 10 > 8
x > -2
8 + 10 > x
18 > x
x < 18
So, x must be longer than 2cm
& shorter than 18cm.
So, there are 3 possibilities.
2 < x < 18

9. ASSIGNMENT:
Page 277 #4-25, 34-36, 43-46

10. ASSIGNMENT:
Page 277 #4-25, 34-36, 43-46