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Home >> Triangle >> Properties >> Sum of Two Sides >>

## 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 ?

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