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[নোটঃ এই আর্টিকেলটি (1) Geometry বিভাগের অধীনে (1) Lines and Angels চ্যাপ্টারের অন্তর্গত, যা 〈1.1.a〉চিহ্ন দিয়ে প্রকাশ করা হয়েছে]

〈1.1〉(a) কোণ সম্পর্কিত প্রাথমিক আলোচনা

Angles

Two lines (রেখা) or line-segments (রেখাংশ) are required to form an angle. An angle is represented by \(\)\angle \(\)  sign .\(\)\angle \(\)\(\)ABC\(\) is an angle below.

Circle
  • A circle has \(\)360\(\)° angles at its center.

  • When two lines intersect, four angles are formed, and the sum of the measures of the angles is \(\)360\(\)°. Similarly when more than two lines intersect, the sum of all the angles is also \(\)360\(\)°.

  • All the angles formed around a point are also \(\)360\(\)°.
Right angle(সমকোণ)

It is a \(\)90\(\)° angle. When two lines are perpendicular, a right angle is formed, and it is expressed with sign. Below is a right angle.

Acute angles (সূক্ষ্ কোণ)

It smaller than \(\)90\(\)°. On the other hand, angles larger than \(\)90\(\)° are called Obtuse angles (স্থূলকোণ)


Here   \(\)\angle \(\)\(\)ABC\(\) is acute but \(\)\angle \(\)\(\)CBD\(\) is obtuse.

Straight angle (সরলকোণ)

It is a \(\)180\(\)°. This is also a straight line, on which a point exists. \(\)\angle \(\)\(\)ABC\(\) is a straight line in the figure below.

Reflex angle (প্রবৃদ্ধ কোণ)

It is larger than \(\)90\(\) but smaller than \(\)180\(\).

Adjacent angles (সন্নিহিত কোণ)

Angles having common vertex and common leg. \(\)\angle \(\)\(\)x\(\) and  \(\)\angle \(\)\(\)y\(\) are adjacent angles in the figure below.

Complementary angles (পূরক কোণ)

These are two adjacent angles whose sum is \(\)90\(\)°. \(\)p\(\) and \(\)q\(\) are complementary in the figure below, because their sum is \(\)90\(\)°. \(\)20\(\)° is the complementary angle for \(\)70\(\)°.

Supplementary angles (সম্পূরক কোণ)

These are two adjacent angles whose sum is \(\)180\(\)°. \(\)s\(\) and \(\)t\(\) are complementary in the figure below, because their sum is \(\)180\(\)°. \(\)120\(\)° is the supplementary angle for \(\)60\(\)°.

Vertical angles (বিপ্রতীপ কোণ)

are formed when two lines intersect. Of the four angles formed, each opposite two are vertical. Vertical angles are equal. In the figure below \(\)a\(\) and \(\)b\(\) are vertical angles.

Corresponding Angles (অনুরূপ কোণ)

Are equal angles, formed on the same side when a non-perpendicular line intersects two parallel lines. In the figure below, line \(\)l\(\) and \(\)m\(\) are parallel and line \(\)k\(\) intersects them. The angles \(\)x\(\) and \(\)y\(\) are corresponding angle and \(\)x\(\) = \(\)y\(\)

Alternate angles (একান্তর কোণ)

These are the equal angles formed on the both side of a non-perpendicular line that intersects a pair of parallel lines. In the figure below, \(\)l\(\) and \(\)m\(\) are parallel lines having a non-perpendicular transversal \(\)k\(\). the angles \(\)x\(\) and \(\)y\(\) formed are called alternate angles.

Straight line (সরল রেখা)

Straight line বা সরল রেখা যে \(\)180\(\)° কোন বিন্দুতে  কোণ উৎপন্ন করে। নীচের ছবিতে দেখুনঃ

Parallel lines (সমান্তরাল রেখা)

এ ধরণের রেখাসমূহ পরষ্পর সমান্তরাল, কখনো পরষ্পরকে ছেদ করে না।

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