Check sibling questions

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

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Here,

Sum of any sides is greater than the third side

AB + AC > BC

AB + BC > AC

BC + AC > AB

 

Let’s take a few examples

 

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

In ∆ABC,

  AB = 6 cm

  BC = 7 cm

  CA = 6 cm

Triangle Inequality - Part 2

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

Triangle Inequality - Part 3

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

Triangle Inequality - Part 4

 

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

 

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.