Key Types of Triangles and Their Properties
You may have come across the word ‘triangle’ several times in your life. You may also know how its shape is and how it varies from a square or a circle. However, this article sheds light on what a triangle is in the context of mathematics.
On top of that, you will also come to know about the triangle and its properties class 7. Therefore, it will make you excited when you find how easy it is to understand the underlying concepts in this chapter. However, first know what a triangle is in a mathematical sense.
What is the Triangle?
Triangles fall under the category of geometry in mathematics. In other words, it has a unique shape that differentiates it from different geometrical shapes that you see in everyday life. However, a triangle is mainly a closed polygon which has three straight sides.
Take a look at the following diagram:
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In this figure, you will see three line segments AB, BC, and AC joined at their ends. Additionally, ‘triangle’ means a figure that has three angles, as you can see in this diagram. The three angles are thus ⊿BAC, ⊿ABC, ⊿ACB.
You will find it intriguing to know that no matter what the angles are in a triangle, their sum is always 1800. Therefore, this polygon can only exist if the total of the internal angles adds up to 1800. You can refer to this phenomenon as sum property of a triangle.
Now, take a look at the types of triangles to understand class 7 the triangle and its properties better.
You can classify the types of triangles in the following categories:
Types of Triangles
The table above concludes the class 7 maths chapter the triangle and its properties. However, you should also know about the additional features of these types of triangles. You can gather knowledge from the following section.
What are the Properties of Triangles?
Take a look at the following triangle and its properties:
The word ‘vertices’ refer to the pointed edges of a triangle.
Always remember that when you add two sides of a triangle, the sum will come out to be higher than the third side’s length.
The side mirroring the largest angle is always the longest line segment in a triangle. In case of right angle triangle, you can call that side as a hypotenuse. The equation to find the hypotenuse is:
(Hypotenuse)2 = (Perpendicular)2 + (Base)2. It is known as the Pythagoras Theorem.
The area of a triangle is = 12 X Height X Base.
The sum of all the line segments in a triangle is known as its perimeter.
The sum of an interior angle and the adjacent exterior angle of a triangle is always 1800
These are the primary triangle and its property. However, try and answer the following questions:
Can a triangle have two right angles?
Can a triangle have two obtuse angles?
Can a triangle have three angles equal to 600?
Now that you know about the triangle and its properties, read about similar interesting topics on Vedantu’s website. You can also download our Vedantu app for enhanced access to these materials.
Other Polygons
Polygons are characterized as closed 2-dimensional shapes that are formed by joining 3 or more line segments with one another. Polygons can be classified as-
Regular Polygons- Regular Polygons are polygons with all of the sides associated with them, tend to be equal, and all the interior angles measure the same. For Example- A Square is a regular quadrilateral or a regular polygon with 4 sides and all its angles are 90 degrees., etc.
Concave Polygons- Concave Polygons are polygons with a minimum of one angle that measures more than 180 degrees. The vertices of these types of polygon tend to be inwards but can also point outwards.
Convex Polygons- Convex Polygons are polygons in which all the interior angles of the figure are less than 180 degrees. Convex Polygons are exactly the opposite of the concave polygon. The vertices of a convex polygon are always towards the out direction.
Trigons- Trigons, also known as Triangles, are polygons that possess three sides. These trigons are divided into different types based on the length of their sides and the measure of their angle. For Example- Equilateral Triangle ( A Trigion with all sides and angles equal), Isosceles triangle ( A trigon with 2 sides and angles equal), etc.
Quadrilateral Polygons- Quadrilateral Polygons is a polygon with 4 sides and 4 vertices. Quadrilateral Polygons are also called Quadrilaterals and Quadrangles. For Example- Square, Rhombus, etc.
Equilateral Polygons- Equilateral Polygons are polygons whose all sides tend to be equal. For Example- Equilateral Triangle, Square, Rhombus, etc.
Equiangular Polygons- Equiangular Polygons are figures with all interior angles equal. For Example- Rectangles, Squares, etc.
Pentagon Polygons- Pentagon polygon is the type of polygon with 5 sides and 5 vertices. Whenever all of the 5 edges of this polygon tend to be equal, then it is also called a regular pentagon.
Hexagon Polygons- Hexagon Polygons is a type of polygon where the shape has 6 sides and 6 vertices. A Regular Hexagon is a polygon that has 6 equal edges and all of its interior and exterior angles also measure equals.
Irregular Polygons- Irregular Polygons are polygons with no particular or unusual form. It represents that the general sides and angles for an Irregular polygon are unequal.
Tips to study Triangles
Triangle is a subtopic of polygons that contains a lot of formulas. To study and bring full marks in Triangles, the student can follow the given tips-
The student should make their own notes and charts of the formulas and properties of different triangles to understand them and use them later during exams.
Students should solve many questions about the topic. They can start by completing the Triangles NCERT Exercises
After completing NCERT, the student can move on to reference books like RD Sharma and RS Aggarwal. They can find solutions to these books at Vedantu's official website.
Students should also go through the previous year's exam papers and solve the Triangle's questions in them. This will help them to break the question pattern and understand the difficulty level of questions asked in an exam.
They can also find a lot of FREE resources like video lectures and a list of important questions that they can get from Vedantu's official website.
Students should practise Triangles seriously as the same topics revisit them in more co plex forms in higher classes.
These are some tips that a student can follow to understand the chapter triangles and get good marks.
FAQs on Triangle and Its Properties Explained
1. What is a triangle in basic geometry?
A triangle is a fundamental two-dimensional shape in geometry. It is a polygon with three straight sides, three corners called vertices, and three interior angles. A key characteristic of any triangle is that the sum of its three interior angles always equals 180 degrees.
2. How are triangles classified based on their sides and angles?
Triangles can be classified in two primary ways:
Based on the length of their sides:
- Equilateral Triangle: All three sides are of equal length.
- Isosceles Triangle: Any two sides are of equal length.
- Scalene Triangle: All three sides have different lengths.
Based on the measure of their angles:
- Acute-angled Triangle: All three interior angles are less than 90°.
- Right-angled Triangle: One of the three angles is exactly 90°.
- Obtuse-angled Triangle: One of the three angles is greater than 90°.
3. What are the three most important properties of a triangle for a Class 7 student?
For Class 7, the three cornerstone properties of a triangle are:
Angle Sum Property: The total of the three interior angles in any triangle is always 180°.
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
Exterior Angle Property: The measure of an exterior angle of a triangle is equal to the sum of its two opposite interior angles.
4. What is the difference between a median and an altitude of a triangle?
While both are lines drawn from a vertex to the opposite side, a median and an altitude have different functions. A median connects a vertex to the midpoint of the opposite side, effectively dividing that side into two equal halves. In contrast, an altitude is a line from a vertex that is perpendicular (forms a 90° angle) to the opposite side. The altitude represents the height of the triangle from that vertex.
5. Why is the Triangle Inequality Theorem important?
The Triangle Inequality Theorem is crucial because it acts as a test to determine if three given lengths can form a triangle. The rule states that the sum of any two sides must be greater than the third side (a + b > c). If this condition isn't met for all three pairs of sides, the sides will not connect to form a closed shape, and a triangle cannot be constructed.
6. What is the Pythagoras property and in which type of triangle does it apply?
The Pythagoras property, also known as the Pythagorean theorem, is a special relationship that applies exclusively to right-angled triangles. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs). The formula is expressed as a² + b² = c², where 'c' is the hypotenuse.
7. Why can a triangle not have two right angles?
A triangle cannot have two right angles because of the Angle Sum Property. The sum of all angles in a triangle must be exactly 180°. If a triangle had two right angles (90° + 90° = 180°), the sum of just those two angles would already be 180°. This would leave 0° for the third angle, which is impossible as a triangle must have three angles to exist.
8. Where can we see examples of triangles being used in real life?
Triangles are fundamental to construction and design because of their inherent strength and stability. Some real-world examples include:
Architecture and Engineering: Roof trusses, bridges (like the Eiffel Tower), and construction cranes use a network of triangles to distribute weight and withstand force.
Navigation: GPS and cell phone towers use a method called triangulation to pinpoint exact locations.
Art and Design: Artists use triangles for creating perspective and balanced compositions in paintings and graphic design.
