Lines and Angles - ESSENTIAL POINTS
- Complementary angles - two angles whose sum is 90°.
- Supplementary angles - two angles whose sum is 180°.
- Adjacent angles - Two angles having a common vertex, a common arm and their non-common arms are on different sides of the common arm.
- Linear pair - If the non-common arms of adjacent angles form a line, they are called a Linear pair.
- Vertically opposite angles - when two lines intersect each other, they form Vertically opposite angles
- If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice-versa.
- If two lines intersect each other, then the vertically opposite angles are equal.
- If a transversal intersects two parallel lines, then
- corresponding angles are equal
- alternate interior angles are equal
- each pair of interior angles on the same side of the transversal are supplementary.
- If a transversal intersects two lines such that, either
- any one pair of corresponding angles is equal
- any one pair of alternate interior angles is equal
- any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.
- Lines which are parallel to a given line are parallel to each other.
- The sum of the three angles of a triangle is 180°.
- If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles
