Properties of Triangles

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Description of the triangles and their characteristics.

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english

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moisés bocanegra castañeda

Colombia

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Properties of TrianglesVersión en línea Description of the triangles and their characteristics. por moisés bocanegra castañeda 1 WHAT IS A TRIANGLE AND ITS PROPERTIES? What is a triangle and its properties? All polygons can be divided into triangles, or in other words, they are formed by combining two or more triangles. Thus, understanding the basic properties of a triangle and their types is essential. 2 TRIANGLE Triangle The triangle is a polygon that has three angles. So, when does a closed figure has three angles? When it has three line segments joined end to end. Thus, we can say that a triangle is a polygon, which has three sides, three angles, three vertices and the sum of all three angles of any triangle equals 180°. 3 PROPERTIES OF A TRIANGLE The properties of a triangle: 1. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. 2. The sum of the length of any two sides of a triangle is greater than the length of the third side. 3. The side opposite to the largest angle of a triangle is the largest side. 4. Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle. 4 TYPES OF TRIANGLES Types of triangles Triangles can be classified in 2 major ways: 1. Classification according to internal angles 2. Classification according to the length of its sides 5 CLASSIFICATION OF A TRIANGLE BY INTERNAL ANGLES CLASSIFICATION OF A TRIANGLE BY INTERNAL ANGLES Based on the angle measurement, there are three types of triangles: 1.Acute Angled Triangle 2.Right-Angled Triangle 3.Obtuse Angled Triangle Let us discuss each type in detail. 6 ACUTE ANGLE TRIANGLE ACUTE ANGLE TRIANGLE A triangle that has all three angles less than 90° is an acute angle triangle. So, all the angles of an acute angle triangle are called acute angles Given below is an example of an acute angle triangle. 7 RIGHT-ANGLE TRIANGLE RIGHT-ANGLE TRIANGLE In a right-angled triangle, the sum of squares of the perpendicular sides is equal to the square of the hypotenuse. For e.g. considering the above right-angled triangle ACB, we can say: (AC)^2 + (CB)^2 = (AB)^2 This is known as Pythagoras theorem Vice versa, we can say that if a triangle satisfies the Pythagoras condition, then it is a right-angled triangle. 8 OBTUSE/OBLIQUE ANGLE TRIANGLE OBTUSE/OBLIQUE ANGLE TRIANGLE A triangle that has one angle that measures more than 90° is an obtuse angle triangle. Given below is an example of an obtuse/oblique angle triangle. 9 CLASSIFICATION OF TRIANGLES BY LENGTH OF SIDES CLASSIFICATION OF TRIANGLES BY LENGTH OF SIDES Based on the length of the sides, triangles are classified into three types: Scalene Triangle. Isosceles Triangle. Equilateral Triangle. Let us discuss each type in detail. 10 SCALENE TRIANGLE SCALENE TRIANGLE A triangle that has all three sides of different lengths is a scalene triangle.Since all the three sides are of different lengths, the three angles will also be different. Given below is an example of a scalene triangle 11 ISOSCELES TRIANGLE ISOSCELES TRIANGLE A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle. The angles opposite the equal sides measure the same. Given below is an example of an isosceles triangle. 12 EQUILATERAL TRIANGLE EQUILATERAL TRIANGLE A triangle which has all the three sides of the same length is an equilateral triangle. Since all the three sides are of the same length, all the three angles will also be equal. Each interior angle of an equilateral triangle = 60° 13 BIBLIOGRAPHY BIBLIOGRAPHY Ashutosh (oct 25, 2020). What is a triangle and its properties? (Definition, types, formulas).e-gmat. recovered from: https://e-gmat.com/blogs/properties-of-triangles/

Properties of TrianglesVersión en línea

Description of the triangles and their characteristics.

por moisés bocanegra castañeda

WHAT IS A TRIANGLE AND ITS PROPERTIES?

What is a triangle and its properties?

All polygons can be divided into triangles, or in other words, they are formed by combining two or more triangles. Thus, understanding the basic properties of a triangle and their types is essential.

TRIANGLE

Triangle

The triangle is a polygon that has three angles. So, when does a closed figure has three angles?

When it has three line segments joined end to end.

Thus, we can say that a triangle is a polygon, which has three sides, three angles, three vertices and the sum of all three angles of any triangle equals 180°.

PROPERTIES OF A TRIANGLE

The properties of a triangle:

1. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

2. The sum of the length of any two sides of a triangle is greater than the length of the third side.

3. The side opposite to the largest angle of a triangle is the largest side.

4. Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

TYPES OF TRIANGLES

Types of triangles

Triangles can be classified in 2 major ways:

1. Classification according to internal angles

2. Classification according to the length of its sides

CLASSIFICATION OF A TRIANGLE BY INTERNAL ANGLES

Based on the angle measurement, there are three types of triangles: 1.Acute Angled Triangle 2.Right-Angled Triangle 3.Obtuse Angled Triangle Let us discuss each type in detail.

ACUTE ANGLE TRIANGLE

A triangle that has all three angles less than 90° is an acute angle triangle. So, all the angles of an acute angle triangle are called acute angles Given below is an example of an acute angle triangle.

RIGHT-ANGLE TRIANGLE

In a right-angled triangle, the sum of squares of the perpendicular sides is equal to the square of the hypotenuse. For e.g. considering the above right-angled triangle ACB, we can say: (AC)^2 + (CB)^2 = (AB)^2 This is known as Pythagoras theorem Vice versa, we can say that if a triangle satisfies the Pythagoras condition, then it is a right-angled triangle.

OBTUSE/OBLIQUE ANGLE TRIANGLE

A triangle that has one angle that measures more than 90° is an obtuse angle triangle. Given below is an example of an obtuse/oblique angle triangle.

CLASSIFICATION OF TRIANGLES BY LENGTH OF SIDES

Based on the length of the sides, triangles are classified into three types: Scalene Triangle. Isosceles Triangle. Equilateral Triangle. Let us discuss each type in detail.

SCALENE TRIANGLE

A triangle that has all three sides of different lengths is a scalene triangle.Since all the three sides are of different lengths, the three angles will also be different. Given below is an example of a scalene triangle

ISOSCELES TRIANGLE

A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle. The angles opposite the equal sides measure the same. Given below is an example of an isosceles triangle.

EQUILATERAL TRIANGLE

A triangle which has all the three sides of the same length is an equilateral triangle. Since all the three sides are of the same length, all the three angles will also be equal. Each interior angle of an equilateral triangle = 60°

BIBLIOGRAPHY

Ashutosh (oct 25, 2020). What is a triangle and its properties? (Definition, types, formulas).e-gmat. recovered from: https://e-gmat.com/blogs/properties-of-triangles/

Properties of Triangles

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CLASSIFICATION OF A TRIANGLE BY INTERNAL ANGLES

ACUTE ANGLE TRIANGLE

RIGHT-ANGLE TRIANGLE

OBTUSE/OBLIQUE ANGLE TRIANGLE

CLASSIFICATION OF TRIANGLES BY LENGTH OF SIDES

SCALENE TRIANGLE

ISOSCELES TRIANGLE

EQUILATERAL TRIANGLE

BIBLIOGRAPHY