1. Inequalities in Triangles

2. Inequalities in Triangles
Triangles have two important properties:
Property #1:
The smallest angle is across from the smallest side (S for Smallest)
The medium angle is across from the medium side (M for Medium)
The largest angle is across from the largest side (L for Largest)

3. Visuals L⁰
**There is no formula to find the side lengths actual measures – you just compare them!
Min
95⁰
9in
Sin
7in
40⁰ S⁰
45⁰ M⁰
Lin
12in

4. Examples
List the sides of the triangle shown in order from least to greatest.
c, a, b

5. More Examples
JK, JL, KL
XY, YZ, XZ
<B, <C, <A
QR, PR=PQ

6. Property #2
Property #2: The two smallest sides of a triangle must add up to be larger than the largest.

7. Examples Can the following side measures be made to form a triangle?
6, 9, 13
4, 8, 12
15, 8, 31
6, 14, 15
10, 10, 8
4, 2, 5
yes no no
yes
yes
yes

8. Examples
To describe the possible lengths of the third side of a triangle given the length of the other two sides: You must write an inequality. There are several solutions!
Example: in., 9 in,
_________< x < __________
(subtract) (add) 3 15

9. More Examples
8 < x < 16
20. 4 ft, 12 ft m, 18 m yd, 16 yd in, 2 ft in, 1 yd
9 < x < 27
5 < x < 37
2in < x < 46in
12in < x < 60 in

10. More Examples
Is it possible to build a triangle using the given side lengths? If so, order the angle measures of the triangle from least to greatest.
Yes: <S, <R, <T
Yes: <B, <C, <A

11. Examples Describe the possible values of x. 2 < 2x -2 < 12