Triangle Inequality Theorem
Understanding and applying the triangle inequality theorem to determine if given side lengths can form triangles and find possible ranges for unknown sides.
Questions
The points $\left( 0,\dfrac { 8 }{ 3 } \right),(1,3)$ and $(82,30)$ are the vertices of:
- an equilateral triangle
- an isosceles triangle
- a right angled triangle
- none of these
In $\Box PQRS$, $PQ+QR+RS+SP> PR+QS$.
- True
- False
The triangle inequality theorem states that
- The sum of the lengths of the $2$ sides of a triangle is equal than the third side of the triangle
- The sum of the lengths of the $2$ sides of a triangle is less than the third side of the triangle
- The sum of the lengths of the $2$ sides of a triangle is more than the third side of the triangle
- None of these
State the following statement is True or False
It is possible to have a triangle of sides $3,4,8$
- True
- False
State the following statement is True or False
The triangle inequality theorem states that the sum of the lengths of the $2$ sides of a triangle is equal than the third side of the triangle
- True
- False
State whether the following statement is True or False.
It is possible to have a triangle of sides $8,10,14$.
- True
- False
A triangle cannot be drawn with the following three sides:
- $2m, 3m, 4m$
- $3m, 4m, 8m$
- $4m, 6m, 9m$
- $5m, 7m, 10m$
If $P$ and $Q$ are represented by complex numbers $z _{1}$ and $z _{2}$ such that $\left| \dfrac { 1 }{ { z } _{ 1 } } +\dfrac { 1 }{ { z } _{ 2 } } \right| =\left| \dfrac { 1 }{ { z } _{ 1 } } -\dfrac { 1 }{ { z } _{ 2 } } \right| $ then the circumference of $\triangleOPQ(O is origin)$ is
- $\dfrac{{ z } _{ 1 } -{ z } _{ 2 } }{2}$
- $\dfrac{{ z } _{ 1 } +{ z } _{ 2 } }{2}$
- $\dfrac{{ z } _{ 1 } +{ z } _{ 2 } }{3}$
- ${ z } _{ 1 } +{ z } _{ 2 } $
The sum of all sides of a quadrilateral is lessthan the sum of its diagonals.
- True
- False