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Triangles| Geometry

Definition: The figure bounded by three line segments is a triangle .The line segments are known as the sides of the triangle. The point common to any two sides is known as vertex. The angle formed at the vertex is an angle of the triangle. The triangle has three sides and three angles.

 

Depending on the lengths of the sides the triangles are of three types:

i) equilateral, ii) Isosceles and iii) Scalene.

 

Equilateral Triangle: A triangle with all three sides equal is called an equilateral triangle. Every angle is equal in equilateral triangle and measure of every angle is 600.

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Isosceles triangle: An isosceles triangle is a triangle that has at least two sides of equal length. The third side is called its base.

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Scalene triangle: A triangle with no sides equal is called a scalene triangle.

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On the basis of the angles, the triangles are also of three types:
i) acute angled, ii) Obtuse angled and iii) Right angled.

Acute angle:A triangle is said to be acute angle triangle when all three of of its angles are acute.

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Right angle triangle: A triangle is said to be right angle triangle when one of its angles is a right angle. Opposite side of right angle of right angle triangle is called hypotenuse. The hypotenuse is the greatest side of a right angled triangle.

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Obtuse angle triangle: A triangle is said to be obtuse angle triangle when one of its angles is obtuse angle.

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Similar triangles: Two triangles are similar triangles if, and only if, (i) three angles of one triangle are congruent to three angles of the second triangles, and (ii) the measures of all corresponding sides are in proportion.

 

Congruency of the two triangles: Two triangles are called congruent triangles if, and only if, all of their corresponding parts are congruent.

 

Perimeter: The sum of the lengths of the sides is called perimeter of the triangle. Generally it is denoted by s.

 

Formula of triangle:

Area of a triangle: ½× base × height.

Or, √s(s-a)(s-b)(s-c)

Area of an equilateral triangle: √3/4a2.

 

 

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If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.

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