Inequalities in Triangles is one of the topics in 9th-grade geometry. There are many theorems in triangle inequality. The name itself says that the triangle inequality describes the relationship between the three sides of the triangle. It states that the sum of lengths of a triangle is greater than the third side.

In this article, you can learn briefly about all the topics of inequalities in triangles. There are many things to learn about these inequalities in the triangles chapter. So we request the students to make use of our page and start preparing for the exams. All you have to do is to click on the given links and solve the problems.

## Inequalities in Triangles Topics List

Check out the topics covered in the Inequalities in triangles chapter. Without knowing the topics you cannot understand the theorems. Enhance your math skills by following our page and prove your best.

- Greater Side has the Greater Angle Opposite to it
- Greater Angle has the Greater Side Opposite to it
- The Sum of any Two Sides of a Triangle is Greater than the Third Side
- Perpendicular is the Shortest Theorem
- Comparison of Sides and Angles in a Triangle
- Problem on Inequalities in Triangle
- Sum Of Any Two Sides Is Greater Than Twice The Median
- Sum of the Four Sides of a Quadrilateral Exceeds the Sum of the Diagonals

### Triangle Inequality Theorem

A triangle inequality theorem states that any two sides of a triangle are more than the third side. Inequalities in triangles discuss about the relationship between all three sides of the triangle.

a < b + c or BC < AB + AC

b < a + c or AC < AB + BC

c < b + c or AB < BC + AC

#### Greater Side has the Greater Angle Opposite to it

Greater Side has the Greater Angle Opposite to it is one of the theorems in this chapter. In this topic, students will learn that in a triangle greater side has a greater angle opposite to that.

#### Greater Angle has the Greater Side Opposite to it

The theorem Greater Angle has the Greater Side Opposite to it states that “the side opposite to the highest angle in the triangle is the longest of all”.

#### The Sum of any Two Sides of a Triangle is Greater than the Third Side

According to this theorem in a triangle, the Sum of two Sides of a Triangle is greater than the third Side. Readout this article to know the details about theorem with proofs.

#### Perpendicular is the Shortest Theorem

Perpendicular is the Shortest is the theorem that proves all the straight lines can be drawn to a straight line from a given point exterior to it.

#### Comparison of Sides and Angles in a Triangle

In this concept, the students of 9th grade can learn more about the sides and angles in a triangle. Students can find problems in the comparison of sides and angles in a triangle.

#### Sum of any two sides is greater than twice the Median

The “Sum of any two sides is greater than twice the Median” is a theorem that states that in a triangle the sum of two sides is higher than two times the median. Have a look at this article to know how it is proven.

#### Sum of the four sides of a Quadrilateral exceeds the sum of the Diagonals

In this article, it is proven that in a quadrilateral the sum of all the four sides is greater than the sum of its diagonals.

### fAQs on Inequalities in triangles

**1. What are inequalities in a triangle?**

Triangle inequality is a Euclidean geometric theorem where the sum of any two sides of a triangle is greater than the third of that triangle.

**2. What are the three inequalities of the triangle?**

The three inequalities in a triangle are as follows,

a < b + c or BC < AB + AC i.e., The sum of AB and AC is greater than BC.

b < a + c or AC < AB + BC i.e., The sum of AB and BC is greater than AC.

c < b + c or AB < BC + AC i.e., The sum of BC and AC is greater than AB.

**3. What is triangle inequality property?**

Triangle inequality property is “The sum of any two sides of a triangle is greater than the third side.”