Types of angles:
(i) Zero Angle: If the initial and final positions of a ray coincide without any rotation, the angle formed is zero angle.
(ii) Right Angle: If the final position of the ray is one fourth of the complete revolution, the angle between the initial and final positions is called right angle.
(iii) Straight Angle: Let OA represents initial position of a ray and 0 B represents the final position such that OA and OB are opposite rays, the angle so formed between opposite rays is a straight angle.
(iv) Complete Angle: If the ray rotates one complete turn and coincides with its initial position then the angle formed is a complete angle.
(v) Acute Angle: An angle whose measure is greater than 0° but less than 90° is called an acute angle.
(vi) Obtuse Angle: An angle whose measure is more than 90° but less than 1800 is called an obtuse angle.
(vii) Reflex Angle: An angle whose measure is more than 180° but less than 360° is called a reflex angle.
Particular types of angles:
(viii) Supplementary Angles: Two angles, whose sum is 180° are called supplementary angles and either is called the supplement of the other.
(ix) Complementary Angles: Two angles, whose sum is 900 are called complementary angles and either is called the complement of the other. .
∠1 + ∠2 = 90°
(x) Adjacent Angles: Two angles one said to adjacent angles if they have
(a) common vertex
(b) a common arm
(c) other arms lying on opposite side of his common arm.
(xi) Congruent or Equal Angles:
Two angles are said to be equal or congruent if and only if the measures of the two angles are the same.
(xii) Linear pair: Two adjacent angles are said to form a linear pair of angles if their non-common arms are two opposite rays.
(xiii) Vertically opposite angles: Any two angles, that are formed by two intersecting lines and which are not adjacent, are called vertically opposite angles. If two lines intersect then vertically opposite angles are always equal.
(xiv) Angle at a point: Let some rays OA, OB, OC, OD and OE having a common initial point O, form ∠1, ∠2, ∠3, ∠4 and ∠5 at 0 then ∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 360°.
Thus, the sum of all angles at a point is 4 right angles.
Transversal: A line that intersects two or more lines at distinct points is called a transversal. AB is a transversal.
1. Interior Angles: The angles labelled 3, 4, 5, 6 are called interior angles.
2. Exterior Angles: The angles labelled 1, 2, 7, 8 are called exterior angles.
3. Corresponding Angles: In the figure, the pair of corresponding angles are : (1,5); (4,8); (2,6); (3,7).
4. Alternate Angles: In the figure, the pair of alternate angles are: (3, 5); (4, 6).
Parallel lines: Two lines are parallel to each other, if
(i) They do not meet, however for they are produced on either side.
(ii) They lie in the same plane, i.e., they are coplanar.
Note:
(1) The distance between two parallel lines is the same at all points. (2) A lie is parallel to itself.
(3) Through a point not on the given line, one and only one line can be drawn parallel to the given line.
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