[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 [latex]\angle [latex] sign .[latex]\angle [latex][latex]ABC[latex] is an angle below.
Circle
- A circle has [latex]360[latex]° angles at its center.
- When two lines intersect, four angles are formed, and the sum of the measures of the angles is [latex]360[latex]°. Similarly when more than two lines intersect, the sum of all the angles is also [latex]360[latex]°.
- All the angles formed around a point are also [latex]360[latex]°.
Right angle(সমকোণ)
It is a [latex]90[latex]° 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 [latex]90[latex]°. On the other hand, angles larger than [latex]90[latex]° are called Obtuse angles (স্থূলকোণ)
Here [latex]\angle [latex][latex]ABC[latex] is acute but [latex]\angle [latex][latex]CBD[latex] is obtuse.
Straight angle (সরলকোণ)
It is a [latex]180[latex]°. This is also a straight line, on which a point exists. [latex]\angle [latex][latex]ABC[latex] is a straight line in the figure below.
Reflex angle (প্রবৃদ্ধ কোণ)
It is larger than [latex]90[latex] but smaller than [latex]180[latex].
Adjacent angles (সন্নিহিত কোণ)
Angles having common vertex and common leg. [latex]\angle [latex][latex]x[latex] and [latex]\angle [latex][latex]y[latex] are adjacent angles in the figure below.
Complementary angles (পূরক কোণ)
These are two adjacent angles whose sum is [latex]90[latex]°. [latex]p[latex] and [latex]q[latex] are complementary in the figure below, because their sum is [latex]90[latex]°. [latex]20[latex]° is the complementary angle for [latex]70[latex]°.
Supplementary angles (সম্পূরক কোণ)
These are two adjacent angles whose sum is [latex]180[latex]°. [latex]s[latex] and [latex]t[latex] are complementary in the figure below, because their sum is [latex]180[latex]°. [latex]120[latex]° is the supplementary angle for [latex]60[latex]°.
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 [latex]a[latex] and [latex]b[latex] 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 [latex]l[latex] and [latex]m[latex] are parallel and line [latex]k[latex] intersects them. The angles [latex]x[latex] and [latex]y[latex] are corresponding angle and [latex]x[latex] = [latex]y[latex]
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, [latex]l[latex] and [latex]m[latex] are parallel lines having a non-perpendicular transversal [latex]k[latex]. the angles [latex]x[latex] and [latex]y[latex] formed are called alternate angles.
Straight line (সরল রেখা)
Straight line বা সরল রেখা যে [latex]180[latex]° কোন বিন্দুতে কোণ উৎপন্ন করে। নীচের ছবিতে দেখুনঃ
Parallel lines (সমান্তরাল রেখা)
এ ধরণের রেখাসমূহ পরষ্পর সমান্তরাল, কখনো পরষ্পরকে ছেদ করে না।
