Properties of Triangles

In trigonometry we will discuss about the different properties of triangles.

We know any triangle has six parts, the three sides and the three angles are generally called the elements of the triangle.

Oblique triangle: A triangle which does not contain right angles is called an oblique triangle.

These six parts are not independent of each other i.e., various relations exist among the six parts.

We will learn how to deduce the relations between the sides and trigonometric ratios of the angles of a triangle.

Let us discuss about some of the properties of triangles.

We know in any triangle ABC, the measures of the angles ∠ABC, ∠BCA and ∠CAB at the vertices B, C and A are denoted by the letters B, C and A respectively. The measures of the sides AB, BC and CA opposite to angles C, A and B respectively are denoted by c, a and b. The perimeter of the triangle is denoted by 2s and semi-perimeter of the triangles denoted by (a + b + c)/2 . The area of the triangle is denoted by ∆ or S. The radius of the circum-circle of the triangle is called the circum-radius and is denoted by R. The radius of the in-circle of the triangle is called the in-radius and is denoted by r. The radius of an ex-circle of the triangle is called an ex-radius and the radii of the ex-circles opposite to the angles A, B, C are denoted by r1, r2, and r3 respectively.

The six elements of a triangle are not independent and are connected by the relations A + B + C = π, a + b > c, b + c > a and c + a > b. In addition to these relations, the elements of a triangle are connected by some trigonometric relations.

 Properties of Triangles




11 and 12 Grade Math

From Properties of Triangles to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More