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

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 ? As we know that Sum of two sides of a triangle is greater than the third side. So, length of third side cannot be greater than the sum of given two sides. Now, we add given two sides and we get: 7 + 9 = 16 Therefore, Third side < 16………….....(statement 1) Also, we know that the difference of two sides of a triangle is smaller than the third side. So, length of third side cannot be smaller than the difference of given two sides. Let's find the difference of given two sides and we get: 9 - 7 = 2 Therefore, Third side >2………….....(statement 1) From Statement 1 and 2, we get: Length of third side can be greater than 2 and less than 16 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 ?