In a triangle,

  Sum of two sides > Third side.

 

In a triangle,

  Sum of two sides is always greater than the third side.

 

For ∆ABC

70.jpg

Here,

Sum of any sides is greater than the third side

AB + AC

AB + BC

BC + AC

 

Let’s take a few examples

 

In following triangles show that, sum of any two sides is greater than the third side.

71.jpg

In ∆ABC,

  AB = 6cm

  BC = 7cm

  CA = 6cm

 

Show that sum of any two sides is greater than the third side

In ∆ABC,

  AB = 6 cm

  BC = 7 cm

  CA = 6 cm

72.jpg

Two sides

Sum of two sides

Third side

Greater

AB, BC

6 + 7  = 13 cm

 CA = 6 cm

Yes

BC, CA

7 + 6 = 13 cm

AB = 6 cm

Yes

AB, CA

6 + 6 = 12 cm

BC = 7 cm

Yes

 

Since sum of any two sides is greater than the third side.

∴ They form a triangle

 

Show that sum of any two sides is greater than the third side

In ∆MON,

  MN = 13 cm

  ON = 5 cm

  OM = 12 cm

73.jpg

Two sides

Sum of two sides

Third side

Greater

MN, ON

13 + 5  = 18 cm

 OM = 12 cm

Yes

ON, OM

5 + 12 = 17 cm

 MN = 13 cm

Yes

MN, OM

13 + 12 = 25 cm

 ON = 5 cm

Yes

Since sum of any two sides is greater than the third side.

∴ They form a triangle

 

Show that sum of any two sides is greater than the third side

In ∆PQR,

  PQ = 8 cm

  QR = 5 cm

  PR = 7 cm

74.jpg

 

Two sides

Sum of two sides

Third side

Greater

PQ, QR

8 + 5  = 13 cm

 PR = 7 cm

Yes

QR, PR

5 + 7 = 12 cm

PQ = 6 cm

Yes

PR, PQ

8 + 7= 15 cm

QR = 5 cm

Yes

 

Since sum of any two sides is greater than the third side.

∴ They form a triangle

 

  1. Chapter 6 Class 7 Triangle and its Properties
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.