Sum of Two Sides of the Triangle is Always Greater than the Third Side

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

This Property can be understood from the below two examples :- Example 1 = Below figure represent Triangle PQR In the above figure, Triangle PQR has PQ = 4.5 cm QR = 8 cm PR = 6 cm Now Lets, check the property PQ + QR > PR 4.5 + 8 > 6 12.5 > 6 ----- (True) QR + PR > PQ 8 + 6 > 4.5 14 > 4.5 ----- (True) PR + PQ > QR 6 + 4.5 > 8 10.5 > 8 ----- (True) Hence, it's proved that "Sum of Two Sides of the Triangle is Always Greater than the Third Side." Example 2 = Below figure represent Triangle ABC In the above figure, Triangle ABC has AB = 4 cm BC = 5 cm CA = 6 cm Now Lets, check the property AB + BC > CA 4 + 5 > 6 9 > 6 ----- (True) BC + CA > AB 5 + 6 > 4 11 > 4 ----- (True) CA + AB > BC 6 + 4 > 5 10 > 5 ----- (True) Hence, it's proved that "Sum of Two Sides of the Triangle is Always Greater than the Third Side." Similarly, we can check and prove that "The difference of two sides of a triangle is smaller than the third side " Study More Solved Questions / Examples Can a triangle be constructed with sides 4 cm, 5 cm & 10 cm ? Can a triangle be formed with sides 6 cm, 7 cm & 3 cm ? In the following diagram, ABC is triangle and D is a point on side BC: In the following quadrilateral: Prove: PQ + QR + PS + RS > PR + QS Lengths of two sides of a triangle are 7 cm and 9 cm. Can you guess between which two numbers will the length of third side fall ?