triangle and its properties
Answers
The properties of a triangle are: A triangle has three sides, three angles, and three vertices. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. The sum of the length of any two sides of a triangle is greater than the length of the third side
Step-by-step explanation:
Types of Triangle
Based on the Sides Based on the Angles
Scalene Triangle Acute angled Triangle
Isosceles Triangle Right angle Triangle
Equilateral Triangle Obtuse-angled Triangle
So before, discussing the properties of triangles, let us discuss types of triangles given above.
Scalene Triangle: All the sides and angles are unequal.
Isosceles Triangle: It has two equal sides. Also, the angles opposite these equal sides are equal.
Equilateral Triangle: All the sides are equal and all the three angles equal to 60°.
Acute Angled Triangle: A triangle having all its angles less than 90°.
Right Angled Triangle: A triangle having one of the three angles exactly 90°.
Obtuse Angled Triangle: A triangle having one of the three angles more than 90°.
Triangle Properties
The properties of the triangle are:
The sum of all the angles of a triangle (of all types) is equal to 180°.
The sum of the length of the two sides of a triangle is greater than the length of the third side.
In the same way, the difference between the two sides of a triangle is less than the length of the third side.
The side opposite the greater angle is the longest side of all the three sides of a triangle.
The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.
Two triangles are said to be similar if their corresponding angles of both triangles are congruent and the lengths of their sides are proportional.
Area of a triangle = ½ × Base × Height
The perimeter of a triangle = sum of all its three sides
Triangle Formula
Area of a triangle is the region occupied by a triangle in a two-dimensional plane. The dimension of the area is square units. The formula for area is given by;
Area = 1/2 x Base x Height
The perimeter of a triangle is the length of the outer boundary of a triangle. To find the perimeter of a triangle we need to add the length of the sides of the triangle.
P = a + b + c
Semi-perimeter of a triangle is half of the perimeter of the triangle. It is represented by s.
s = (a + b + c)/2
where a, b and c are the sides of the triangle.
By Heron’s formula, the area of the triangle is given by:
A = √[s(s – a)(s – b)(s – c)]
where ‘s’ is the semi-perimeter of the triangle.
By the Pythagorean theorem, the hypotenuse of a right-angled triangle can be calculated by the formula:
Hypotenuse2 = Base2 + Perpendicular2