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# Triangles Formulas Class 10

Triangles formulas class 10 are important to understand the concept of similarity and congruence of various shapes. These formulas define the difference between congruence and similarity by applying the relevant principles. Therefore, students should possess precise knowledge of all concepts before proceeding to solve problems based on them. To help students establish a clear understanding of all triangles related formulas, this article provides a list of Triangles formulas class 10 along with some examples.

## List of Triangles Formulas Class 10

Students can refer to the list of triangle formulas class 10 provided below:

**Similarity of Triangles**

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio (or proportion).

**Ratio of Sides of Similar Triangles**

The ratio of the sides of two triangles, ABC and XYZ, which are similar, is equal.

E.g., For identical triangles ABC and XYZ, AB/XY= BC/YZ= CA/ZX.

**Area of Similar Triangles:**

If two triangles, ABC and XYZ, are similar, then,

Area of triangle ABC/ Area of triangle XYZ = (AB)^{2}/ (XY)^{2} = (BC)^{2}/ (YZ)^{2} = (AC)^{2}/ (XZ)^{2}

**Inequality in Triangles:**

The sum of two sides is always greater than the third side: AB + BC > AC.

## Applications of Triangles Formulas Class 10

The similarity and congruence principles play an important role in various sciences. Thus, triangles formulas are applied in various fields to perform numerous calculations. Here are some of the applications of triangles formulas class 10:

- Civil engineers use triangles formulas class 10 to make a strong structure that is unaffected by severe weather conditions.
- In geography, these formulas are applied to evaluate the sizes of objects which are difficult to measure by hand, for example, height of a mountain, or the distance to the moon.

## Tips to Memorize Triangles Formulas Class 10

The following tips will assist students to relieve the stress of learning and memorizing triangles formulas class 10:

- Students should properly read the explanation of formulas along with important notes and examples provided in their textbooks to learn all fundamental principles.
- They can find some useful study material online for revision of formulas and for clarifying their doubts. This will not only make studying easier and more enjoyable, but it will also help learning problem-solving.
- Formulas images can also be used on handheld devices like mobile phones and tablets for revision. It will make revision easy.

## Triangles Formulas Class 10 Examples

**Example 1:** Two triangles have equal area, can you verify if they are congruent too?

**Solution:** For any two triangles to be similar their corresponding angles should be equal and the ratio of their sides should be the same.

We know that the ratio of area of similar triangles is equal to the ratio of squares of corresponding sides.

Since, the area of triangles is equal, the ratio of square of corresponding sides of triangles = 1

As per SSS theorem, if the ratio of sides is equal the triangles are congruent.

Thus, triangles having the same area also have the same ratio of corresponding sides and are thus congruent.

**Example 2:** The length of three sides of triangle ABC is AB =3 , BC = 4 and AC = 5. Determine if it is a right angled triangle?

**Solution :** We know that in a right angled triangle, if the square of one side is equal to the sum of the squares of the other two sides and the angle opposite to the first side is a right angle.

To verify this, the sides AB, BC and AC have to be a part of the pythagorean triplet.

i.e., AB^{2} + BC^{2} = AC^{2} = 3^{2} + 4^{2} = 5^{2},

⇒ 9 + 16 = 25

⇒ 25 = 25

Thus, it is a right-angled triangle so the biggest angle in the triangle is 90 degrees.

Students can download the printable **Maths Formulas Class 10** sheet from below.

## FAQs on Triangles Formulas Class 10

### What are the Important Formulas Covered Under Triangles Formulas Class 10?

The important formulas covered under triangles formulas class 10 are as follows:

- Ratio of the sides of two triangles, ABC and XYZ, which are similar, is equal.

E.g., For identical triangles ABC and XYZ, AB/XY= BC/YZ= CA/ZX.

- Inequality in triangles: The sum of two sides is greater than the third side: AB+ BC > AC.
- If two triangles, ABC and XYZ, are similar, then

Area of triangle ABC/ Area of triangle XYZ = (AB)^{2}/ (XY)^{2} = (BC)^{2}/ (YZ)^{2} = (AC)^{2}/ (XZ)^{2}

### Why is it Important to Solve Problems Related to the Triangles Formulas Class 10?

Solving formulas related to triangle formulas class 10 will enable students to understand the concept of ratio between sides of similar triangles, triangle inequality and area of similar triangles. The basic formulas in triangles formulas class 10 also cover the theorems regarding triangle similarity and congruence.

### How Many Formulas are There in Triangles Formulas Class 10?

There are around three major formulas in triangles formulas class 10 which cover triangle similarity and congruence, area of similar triangles, and proof of Pythagoras theorem using congruence and similarity theorems. In order to score well in the examinations, one must understand these formulas thoroughly.

### How can I Memorize Triangles Formulas Class 10?

The following tips will assist students to relieve the stress of learning triangles formulas class 10:

- Students should attempt to solve all of the solved examples in their textbooks, as these examples are intended to cover all of the fundamental principles.

- In addition, students must download formula images from the internet. These can be used as a screensaver on their laptops and mobile phones. This will serve as a reminder to revise the formulas.

- Group studies can also benefit students to get their doubts cleared easily. Discussing these formulas with friends will relieve stress and make the learning process more enjoyable.

### How to Download the Triangles Formulas Class 10 pdf?

Students can download the triangles formulas class 10 pdf through the option provided on this page. They need to follow a few simple steps to download these formulas.

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