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., AB² + BC² = AC² = 3² + 4² = 5²,

⇒ 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.