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5c2. Triangles and other Polygons

A triangle is formed by joining three non-collinear points. It has three sides and three angles. The sums of the angles of a triangle add up to 180 degree. Triangles are classified according to the relative length of their sides and measure of angles.


A scalene triangle has all three sides unequal.


An isosceles triangle has two sides equal.


An equilateral triangle has all three sides equal. Each Interior angle is equal to 600.


An acute triangle is one in which all three interior angles are acute angles.


An obtuse triangle is one in which one interior angle is an obtuse angle. Since the sum of all the angles in a triangle is 180, the other two angles will be acute.


A right-angled triangle is one in which one interior angle is a right triangle.


Polygons


A polygon is a closed figure in a plane. The number of angles or the sides identifies the polygons. Thus, a polygon with 3 angles or 3 sides is a triangle; with 4 angles or 4 sides is a quadrilateral and so on.


Pentagon – 5 sided
Hexagon – 6 sided
Heptagon – 7 sided
Octagon – 8 sided
Nonagon – 9 sided
Decagon – 10 sided
Dodecagon – 12 sided


The different kinds of Polygons are


1. Quadrilaterals
2. Parallelogram
3. Rhombus
4. Rectangle
5. Square
6. Trapezoid


Examples


1. ABC is a right-angled isosceles triangle, right angled at B, and AB = BC = a. Line BD is perpendicular to AC. Then BD is equal to:




Solution: Since AB = BC  D is the mid point of AC, i.e., AD = DC



 








 
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