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

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

In the following diagram, ABC is triangle and D is a point on side BC: In the given diagram, join A and D and we get: After joining A and D we get two triangles: △ ABD △ ACD In △ ABD, we have following sides: AB, BD, AD Apply the property Sum of two sides of a triangle is greater than the third side and we get the following statement: AB + BD > AD .......…...(Statement 1) Now, in △ ACD, we have following sides: CA, CD, AD Apply the property "Sum of two sides of a triangle is greater than the third side" and we get the following statement: CA + CD > AD .......…...(Statement 2) Add statement 1 & statement 2 and we get: AB + BD + CA + CD > AD + AD We can also write it as: AB + BD + CD + CA > AD + AD Now you can see that if on joining BD and CD we get BC: AB + BC + CA > AD + AD And add AD + AD and we get: AB + BC + CA > 2AD (Hence proved) Related Question 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 ?