Angle opposite to longer side is greater

Sum of Two Sides	Angle Sum Property	Angles opposite to equal sides of triangle are equal	Angle opposite to longer side is greater	Pythagoras Theorem
Exterior Angle Property of a Triangle	Mid point property of Triangle	Triangles on same base & between same parallel lines

Let's first understand what does this property of triangle explains ? Observe the following diagram: AB is the longest side of triangle ABC. Angle opposite to side longest AB is Angle C (highlighted in pink in the below diagram) So, as per the given property of triangle, which says, "angle opposite to longer side of a triangle is greater"; we can conclude that: Angle C is the greatest angle in given triangle ABC (because it's opposite side AB is the longest side). How to prove this property of triangle ? Observe the following diagram: Three sides of the given triangle ABC are AB, BC and CA On measuring the length of these three sides we get: AB > CA > BC ..... (Statement 1) Let's find angles opposite to sides AB, BC and CA: Angle opposite to side AB is Angle C Angle opposite to side BC is Angle A Angle opposite to side CA is Angle B Now, measure all the angles and we get: ∠ C > ∠ B > ∠ A .....(statement 2) From statement 1 and 2, we get that: AB is the longest side and it's opposite Angle C is the greatest angle. Hence, this proves the property, angle opposite to longer side of a triangle is greater Also, from statement 1 and 2, we can also conclude: BC is the smallest side and it's opposite Angle A is the least angle. And we obtain another property, angle opposite to smaller side of a triangle is lesser Also, with the above two properties, we can conclude a converse property: In a triangle, side opposite to greater angle is longer and side opposite to lesser angle is smaller