Facts that Matter: Triangles

# Facts that Matter: Triangles | Mathematics (Maths) Class 10 PDF Download

A Triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

Any polygon which has three sides and three vertices is known as Triangle

## Types of Triangles

1. There are three types of Triangles on the basis of the length of the sides.

2. There are three types of Triangles on the basis of angles.

Note:

• Sum of Angles: In any triangle, the sum of all three interior angles always equals 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.
• Heron's Formula: Heron's formula can be used to find the area of a triangle when the lengths of all three sides are known. The formula is given by A = √(s(s-a)(s-b)(s-c)), where 's' is the semi-perimeter of the triangle and 'a', 'b', and 'c' are its side lengths.

Question for Facts that Matter: Triangles
Try yourself: What does 's' represent in Heron's formula A = √(s(s-a)(s-b)(s-c)?

## Area of Triangle

The area of a triangle A is half the product of its base b and its height ℎ
The height of a triangle is also known as the altitude. This formula works only if the base is perpendicular to the height. That means the base and the height form a right angle.

## Congruent Triangles

When two triangles are congruent, it means they look exactly the same. All their sides have the same lengths, and all their angles are the same size. You can move, turn, or flip them, and they will still match up perfectly. There are four ways to check if triangles are congruent. Even if you only know some of their measurements, you can still tell if they're the same.

### Difference B/W Congruent & Similar Triangle

Two triangles are said to be congruent if they are of the same shape and size whereas two triangles are said to be similar if they are of the same shape but can be of different sizes.

Question for Facts that Matter: Triangles
Try yourself:
What is the formula for the area of a triangle?

## Important Formulas

Q1: How many different kinds of triangles exist in Mathematics?

Ans: There are six main types of triangles. They are:

(i) Scalene Triangles

(ii) Isosceles Triangles

(iii) Equilateral Triangles

(iv) Acute Triangles

(v) Obtuse Triangles

(vi) Right Triangles

Q2: What is the formula for area and perimeter of a triangle?

Ans: The perimeter of triangle = Sum of all three sides

Area = ½ (Product of base and height of a triangle)

The document Facts that Matter: Triangles | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Facts that Matter: Triangles - Mathematics (Maths) Class 10

 1. What are the three types of triangles based on their sides?
Ans. The three types of triangles based on their sides are: 1. Scalene triangle: A triangle with no sides equal in length. 2. Isosceles triangle: A triangle with two sides equal in length. 3. Equilateral triangle: A triangle with all three sides equal in length.
 2. How many types of triangles are based on their angles?
Ans. Triangles can be classified into three types based on their angles: 1. Acute triangle: A triangle with all three angles less than 90 degrees. 2. Right triangle: A triangle with one right angle measuring 90 degrees. 3. Obtuse triangle: A triangle with one angle greater than 90 degrees.
 3. What is the sum of the angles in a triangle?
Ans. The sum of the angles in a triangle is always 180 degrees. This property is known as the angle sum property of triangles.
 4. What is the Pythagorean theorem?
Ans. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It can be written as: a^2 + b^2 = c^2, where 'c' represents the length of the hypotenuse, and 'a' and 'b' represent the lengths of the other two sides.
 5. How can we determine if two triangles are similar?
Ans. Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. This means that the ratio of the lengths of the corresponding sides of the triangles will be equal. Similar triangles have the same shape but may differ in size.

## Mathematics (Maths) Class 10

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