Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Facts that Matter: Triangles
Facts that Matter: Triangles | Mathematics (Maths) Class 10 PDF Download
| Table of contents |
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| Types of Triangles |
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| Area of Triangle |
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| Congruent Triangles |
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| Important Formulas |
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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: TrianglesTry yourself: What does 's' represent in Heron's formula A = √(s(s-a)(s-b)(s-c)?
View Solution
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: TrianglesTry yourself: What is the formula for the area of a triangle?View Solution
Important Formulas
Frequently Asked Questions
Q1: How many different kinds of triangles exist in Mathematics?
Ans: There are six main types of triangles. They are:
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)
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FAQs on Facts that Matter: Triangles - Mathematics (Maths) Class 10
| 1. What are the different types of triangles based on their angles and sides? |  |
Ans. Triangles can be classified based on their angles and sides. By angles, they can be acute (all angles less than 90°), right (one angle equal to 90°), or obtuse (one angle greater than 90°). By sides, they can be equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal).
| 2. How do you calculate the area of a triangle? | |
Ans. The area of a triangle can be calculated using the formula: Area = 1/2 × base × height. Alternatively, if you know the lengths of all three sides (a, b, and c), you can use Heron's formula: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter (s = (a + b + c) / 2).
| 3. What does it mean for triangles to be congruent? | |
Ans. Triangles are congruent if they have the same shape and size. This can be established through several criteria, including Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles.
| 4. What are some important formulas related to triangles that I should know? | |
Ans. Important formulas related to triangles include:
1. Area = 1/2 × base × height
2. Perimeter = a + b + c (where a, b, and c are the lengths of the sides)
3. Pythagorean theorem (for right triangles): a² + b² = c²
4. Angle sum property: The sum of the interior angles of a triangle is always 180°.
| 5. What facts about triangles are essential for solving problems in geometry? | |
Ans. Essential facts about triangles include:
1. The longest side of a triangle is opposite the largest angle.
2. The smallest angle is opposite the shortest side.
3. The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the remaining side.
4. The area and perimeter formulas are crucial for various geometry problems involving triangles.
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