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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 "


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