Question

Show whether the inequality theroom
applicable
to this triangle
or not​

Answer 1

Answer:

578766-665_&+::-(;: RT Nagar gohalpur to you the answer is no e captain ko hatao Bharat ki baat karte hai aap ki

Answer 2

Answer:

According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side. A polygon bounded by three line-segments is known as the Triangle. It is the smallest possible polygon. A triangle has three sides, three vertices, and three interior angles. The types of triangles are based on its angle measure and length of the sides. The inequality theorem is applicable for all types triangles such as equilateral, isosceles and scalene. Now let us learn this theorem in details with its proof.

Step-by-step explanation:

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side. In other words, this theorem specifies that the shortest distance between two distinct points is always a straight line.

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

Proof of triangle inequality theorem

S.No Statement Reason

1. |CD|= |AC| + |AD| From figure 3

2. |CD|= |AC| + |AB| AB = AD, ∆ADB is an isosceles triangle

3. ∠DBA <∠DBC Since ∠DBC = ∠DBA+∠ABD

4. ∠ADB<∠DBC ∆ADB is an isosceles triangle and ∠ADB = ∠DBA

5. |BC|<|CD| Side opposite to greater angle is larger

6. |BC|<|AC| + |AB| From statements 3 and 4

Thus, we can conclude that the sum of two sides of a triangle is greater than the third side.