The document discusses theorems related to triangle inequalities. It categorizes theorems into those involving one triangle or two triangles. For one triangle, it lists four theorems including the triangle inequality theorem and exterior angle inequality theorem. For two triangles, it mentions the hinge theorem and converse hinge theorem. It also provides examples applying the exterior angle theorem to find unknown angles.

2. •THEOREMS ON TRIANGLE INEQUALITIES
ARE CATEGORIZED INTO TWO. THESE ARE
THE INEQUALITIES IN ONE TRIANGLE AND
INEQUALITIES IN TWO TRIANGLES

3. . FOR INEQUALITIES IN ONE TRIANGLE
THE FOLLOWING THEOREMS APPLY:
•1. TRIANGLE INEQUALITY THEOREM 1 (𝑆𝑠 → 𝐴𝑎)
•2. TRIANGLE INEQUALITY THEOREM 2 (𝐴𝑎 → 𝑆𝑠)
•3. TRIANGLE INEQUALITY THEOREM 3 (𝑆1 + 𝑆2 > 𝑆3)
•4. EXTERIOR ANGLE INEQUALITY THEOREM.

4. INEQUALITIES IN TWO TRIANGLES
USE EITHER OF THESE THEOREMS:
1. HINGE THEOREM OR SAS INEQUALITY THEOREM
2. CONVERSE OF HINGE THEOREM OR SSS INEQUALITY
THEOREM

5. Example 1
List down the angles of ∆𝐺𝑂𝑇 from greatest to least measure. (Note: The figure is not
drawn to scale.)

12. •WHEN THE SIDES OF A POLYGON
ARE EXTENDED, OTHER ANGLES
ARE FORMED.
•THE ORIGINAL ANGLES ARE THE
INTERIOR ANGLES.
•THE ANGLES THAT FORM LINEAR
PAIRS WITH THE INTERIOR ANGLES
ARE THE EXTERIOR ANGLES.
Angles

14. EXTERIOR ANGLE THEOREM
AN EXTERIOR ANGLE OF A TRIANGLE…
… IS EQUAL IN MEASURE TO THE SUM OF THE MEASURES OF ITS TWO REMOTE
INTERIOR ANGLES.
remote
interior
angles Exterior angle

15. EXTERIOR ANGLE THEOREM
THE MEASURE OF AN EXTERIOR ANGLE IN A TRIANGLE IS THE SUM OF THE
MEASURES OF THE 2 REMOTE INTERIOR ANGLES
3
2
1 4
exterior
angle
remote
interior
angles
m<1 + m<2 = m<4

16. EXAMPLES
m<G = 180 - (60 + 69)
m<FHG = 180 – 111 = 69 linear pair

17. EXAMPLES
x
82°
30° y
Find x & y
x = 68°
y = 112°
y = 30 + 82
y = 112˚
180 = 30 + 82 + x
180 = 112 + x
68˚ = x

18. EXAMPLES
FIN
D
m JKM

2x – 5 = x + 70
x – 5 = 70
x = 75
m< JKM = 2(75) - 5
m< JKM = 150 - 5
m< JKM = 145˚