LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

GEOMETRY-TRIANGLE-INEQUALITIES-IN-A-TRIANGLE

__INEQUALITIES IN A TRIANGLE –__

__Inequality
1)__ –

**If two sides
of a triangle are considered unequal, then the greater side has the greater
angle just opposite to it.**

**In the figure, AC > AB, **

**SO, ∠ABC > ∠ACB**

__Converse -__

**In a triangle, the side just opposite to the greater angle is considered to be greater**

**In the figure, ∠ABC > ∠ACB,**

**So, AC > AB**

**Inequality 2) –**

**Any two sides of any triangle that are together will
be considered greater than the third side of the triangle.**

**In other words, in any ∆ ABC, AB + AC > BC,**

** BC + BA > CA,**

** CA + CB > AB**

**Inequality 3) –**

**The difference between any two sides of a triangle is considered
smaller than the third side of the said triangle.**

**In the figure, AC – AB < BC,**

** BC – AC < AB,**

** BC – AB < AC**