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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| Triangles |
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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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Triangles
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)?
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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.
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Difference B/W Congruent & Similar Triangle
Two shapes that have the same form (but not necessarily the same size) are known as similar figures. All congruent figures are similar, but the reverse is not true. Two triangles are considered congruent if they have the same shape and size. On the other hand, two triangles are similar if they share the same shape but can differ in size.
Question for Facts that Matter: Triangles
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What is the formula for the area of a triangle?View Solution
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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 sides? |  |
| 2. How do you calculate the area of a triangle? | |
Ans.The area of a triangle can be calculated using the formula:
Area = (base × height) / 2.
Here, the base is the length of one side, and the height is the perpendicular distance from the opposite vertex to that base.
| 3. What are congruent triangles and how can they be identified? | |
Ans.Congruent triangles are triangles that are identical in shape and size. They can be identified using several criteria including:
1. Side-Side-Side (SSS) Criterion: If all three sides of one triangle are equal to the three sides of another triangle.
2. Side-Angle-Side (SAS) Criterion: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
3. Angle-Side-Angle (ASA) Criterion: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
| 4. What are some important formulas related to triangles? | |
Ans.Some important formulas related to triangles include:
1. Area = (base × height) / 2
2. Perimeter = sum of all sides
3. Pythagorean Theorem (for right triangles): a² + b² = c², where c is the hypotenuse.
4. Heron's Formula for area: Area = √[s(s - a)(s - b)(s - c)], where s = (a + b + c) / 2 and a, b, c are the sides of the triangle.
| 5. Why is it important to understand the properties of triangles? | |
Ans.Understanding the properties of triangles is important because they are fundamental shapes in geometry and are used in various fields such as architecture, engineering, and art. Mastery of triangle properties aids in solving complex geometric problems and is essential for understanding more advanced concepts in mathematics.
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