Question

write two theorem of inequality of triangle ​

Answer 1

Answer:

Hence, let us check if the sum of two sides is greater than the third side. Therefore, the sides of the triangle do not satisfy the inequality theorem.

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Q. 3: If the two sides of a triangle are 2 and 7. Find all the possible lengths of the third side.

Answer 2

Answer:

Consider a ∆ABC as shown below, with a, b and c as the side lengths.

Triangle Inequality Theorem

The triangle inequality theorem states that:

a < b + c,

b < a + c,

c < a + b

In any triangle, the shortest distance from any vertex to the opposite side is the Perpendicular. In figure below, XP is the shortest line segment from vertex X to side YZ.

Triangle Inequality Theorem Proof

Let us prove the theorem now for a triangle ABC.

Triangle Inequality Theorem Derivation - 1

Triangle ABC

To Prove: |BC|< |AB| + |AC|

Construction: Consider a ∆ABC. Extend the side AC to a point D such that AD = AB as shown in the fig. below.

Triangle Inequality Theorem Derivation - 2