Lines and Angles-Notes

1.  Two angles are called adjacent angles if

      (a)   they have the same vertex.

      (b)   they have a common arm and

      (c)   uncommon arms are on either side of the common arm.

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

3.  The sum of all the angles round a point is equal to 360°.

4.  If two lines intersect, then the vertically opposite angles are equal.

5.  A line which intersects two or more given lines at distinct points, is called a transversal of the lines.

6.  Two angles on the same side of a transversal are known as corresponding angles if both lie either above the two lines or below the two lines.

7.  The pairs of interior angles on the same side of the transversal are called consecutive interior angles.

8.  If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.

9.  If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal.

10.  If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.

11.  A triangle whose sides are unequal, is called a scalene triangle.

12.  A triangle, two of whose sides are equal in length, is called an isosceles triangle.

13.  A triangle, all of whose sides are equal is called an equilateral triangle.

14.  A triangle, each of whose angle is less than 90°, is called an acute triangle.

15.  A triangle with one of its angle 90°, is called a right triangle.

16.  A triangle with one of its angle greater than 90°, is known’s an obtuse triangle.

17.  If a side of a triangle is produced, the exterior angle so formed is equal to the sum of two interior opposite angles.

18.  If all sides of a polygon are equal, it is called a regular polygon.

19.  Sum of all the interior angles of a polygon of n sides = (n – 2) × 180°, (n ≥ 3)

20.  Each interior angle of a regular polygon on n sides

21.  Sum of all the exterior angles formed by producing the sides of polygon = 360°

22.  Number of sides of polygon