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short notes on trigonometry properties of triangles

short notes on trigonometry properties of triangles
 

Grade:9

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
A triangle having all the three sides of equal length is an equilateral triangle.
A triangle having two sides of equal length is an Isosceles triangle.
A triangle having three sides of different lengths is called a scalene triangle.
A triangle whose all angles are acute is called an acute-angled triangle or Acute triangle.
A triangle whose one angle is obtuse is an obtuse-angled triangle or Obtuse triangle
A triangle whose one angle is a right-angle is a Right-angled triangle or Right triangle.
For a Right triangle ABC,
BC^2 = AB^2 + AC^2
The sum of the angles in a triangle is 180°. This is called the angle-sum property.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.
The side opposite to the largest angle is the longest side of the triangle and the side opposite to the smallest angle is the shortest side of the triangle.
An exterior angle of a triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.
Two triangles are said to be similar if the corresponding angles of two triangles are congruent and lengths of corresponding sides are proportional.
Side-Side-Side (SSS) criterion for similarity:
If three sides of a triangle are proportional to the corresponding three sides of another triangle then the triangles are said to be similar.
 Side-Angle-Side (SAS) criterion for similarity:
If the corresponding two sides of the two triangles are proportional and one included angle is equal to the corresponding included angle of another triangle then the triangles are similar.
Angle-Angle-Angle (AAA) criterion for similarity:
If the three corresponding angles of the two triangles are equal then the two triangles are similar.
Two triangles are said to be congruent if all the sides of one triangle are equal to the corresponding sides of another triangle and the corresponding angles are equal.
The Area of a triangle is given by the formula
Area of a triangle = (1/2) *Base * Height

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