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CBSE - IX
Parallel Lines
Two lines having only one point in common are called intersecting lines
Two lines in the same plane are parallel if they are equidistant.
A line that intersects two or more lines, at a different points is called a Transversal
When a transversal intersects two lines, eight angles are formed, four angles at each point, P and Q respectively.
We identify these angles by their positions.
∠ 1, ∠ 2, ∠ 7 and ∠ 8 are called exterior angles
∠ 3, ∠ 4, ∠ 5 and ∠ 6 are called Interior angles
∠ 1 and ∠ 5 , ∠ 2 and ∠ 6,∠ 4 and ∠ 8 ,∠ 3 and ∠ 7 are Pair of corresponding angles
∠ 1 and ∠ 7 , ∠ 2 and ∠ 8 are pair of alternate exterior angles
∠ 4 and ∠ 6 , ∠ 3 and ∠ 5 are Pair of alternate interior angles
∠ 4 and ∠ 5 , ∠ 3 and ∠ 6 are Consecutive Interior angles on the same side of the transversal
When a transversal intersects two lines
Pair of corresponding angles is equal
Pair of alternate exterior angles is equal.
Pair of alternate interior angles is equal.
Consecutive interior angles on the same side of the transversal are supplementary.
Theorem: If a transversal intersects two parallel lines, then each pair of corresponding angles are equal
Theorem: If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
Theorem: If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
Theorem: If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
Theorem: If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
Theorem: If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.
Lines which are parallel to the same line are parallel to each other.
Theorem: The sum of three angles of a triangle is 1800.
Theorem: In a triangle if a side is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
