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CBSE Lines and Angles Class 9th Formula .

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An angle is formed by two rays originating from same point. The rays making an angle are called arms of the angle and the point is called vertex of the angle.

Right angle : An angle whose measure is 90° is called a right angle.

Acute angle: An angle whose measure is less than 90° is called an acute angle.

Obtuse angle  : An angle whose measure is more than 90° but less than 180° is called an obtuse angle.

Straight angle : An angle whose measure is 180° is called straight angle.

Reflex angle: An angle whose measure is more than 180° but less than 360° is called reflex angle.

Complete angle : An angle whose measure is 360° is called complete angle.

•Two angles are said to be complementary if their sum is 90°.Two angles are said to be  supplementary  if their sum is 180°.

•Two angles having a common vertex and a common arm are called adjacent angles if their non-common arms are on either side of the common arm.

• Two angles are said to form a linear pair of angles, if their non- common arms are the two opposite rays.

• Two angles are pair of vertically opposite angles if their arms form two pairs of opposite rays.

• If two lines intersect each other, then pair of vertically opposite angles formed are equal.

• If a transversal intersects two parallel lines, then each pair of:

(i)  corresponding angles are equal.

(ii) alternate interior angles are equal.

(iii) interior  angles  on  the  same  side  of  transversal  are supplementary.

• If a transversal intersects two lines such that any pair of corresponding angles are equal then the lines are parallel.

• If a transversal intersects two lines such that one pair of alternate interior angles are equal, then the lines are parallel.

• If a transversal intersects two lines such that any one pair of interior angles on the same side of transversal are supplementary then the lines are parallel.

• Lines which are parallel to a given line are parallel to each other.

• Lines which are perpendicular to a given line are parallel to each other.

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