# How do you prove that the sum of two sides is greater than the third?

## How do you prove that the sum of two sides is greater than the third?

∠ABD>∠CDB. Hence we have AD>AB( because the side opposite to a larger angle is longer). AD = AC+BC. Hence the sum of two sides of a triangle is larger than the third side.

### Why must the sum of two sides of a triangle be greater than the third side?

In order to draw a triangle, the sum of the lengths of any of the two segments must be greater than the length of the third segment. that a + b is not greater than c. The sum of the lengths of any two sides of a triangle must be greater than the third side.

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#### Is the difference of two sides of a triangle is less than the third side?

We know that the definition of a triangle as the polygon having three sides such that the sum of any two sides is greater than the third side. Therefore, we can say that the difference between two sides is less than the third side.

What is the sum of the squares of two sides of a triangle?

When the sum of the squares on two sides of a triangle is equal to the square on the third side, then the triangle is right angled .

Which side of triangle is greater?

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangle Inequality: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side.

## When the sum of the squares of the length of two sides of a triangle is equal to the square of the length of the third side it is called triangle?

The converse of the Pythagorean Theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

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### What is the statement of the triangle inequality theorem?

triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

#### What is the triangle sum theorem?

Theorem: The sum of the measures of the interior angles of a triangle is 180°.

Is the sum of two sides of a triangle twice the median?

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side. Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side. Hence the sum of any two sides of a triangle is greater than twice the median with respect to the third side.

Is the sum of two sides of a triangle always greater?

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In a triangle, Sum of two sides is always greater than the third side.

## What is the sum of two sides > the third side?

Sum of two sides > Third side. Sum of two sides is always greater than the third side. Since sum of any two sides is greater than the third side. Since sum of any two sides is greater than the third side. Since sum of any two sides is greater than the third side.

### How do you prove the perimeter of a triangle is greater?

Prove that the perimeter of a triangle is greater than the sum of its three medians. Prove that if two sides of a triangle are unequal, the longer side has greater angle opposite it. In the figure PQ > PR, QS and RS are the bisectors of Q and R respectively.