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
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
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
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
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