Notes On Parallel Lines - CBSE Class 9 Maths

Intersecting lines
Two lines having only one point in common are called intersecting lines

Parallel lines
Two lines drawn in a plane are parallel if they do not intersect even when they are produced. Distance between the parallel lines is the same.

Transversal
A line that intersects two or more lines, at different points is called a transversal.


When a transversal intersects two lines, m and n, eight angles are formed, four angles at each point, P and Q respectively. These angles are identified 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 pairs of corresponding angles
        •  ∠1 and ∠7,  ∠2 and ∠8 are pairs of alternate exterior angles
        •  ∠4 and ∠6, ∠3 and ∠5 are pairs of alternate interior angles
        •  ∠4 and ∠5, ∠3 and ∠6 are consecutive interior angles on the same side of the transversal


Lines, Intersecting lines, . Parallel lines, Transversal, Exterior angles, Interior angles , Corresponding angles, Alternate interior angles, Consecutive Interior angles, allied interior angles , co-interior angles

If a transversal intersects two parallel lines, then
        •  each pair of corresponding angles is equal.
        •  each pair of alternate interior angles is equal.
        •  each pair of interior angles on the same side of the transversal is supplementary

Two lines intersected by a transversal are parallel if, either
        •  any one pair of corresponding angles is equal, or
        •  any one pair of alternate interior angles is equal, or
        •  any one pair of interior angles on the same side of the transversal is supplementary

Lines which are parallel to the same line are parallel to each other.

The sum of 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.

Summary

Intersecting lines
Two lines having only one point in common are called intersecting lines

Parallel lines
Two lines drawn in a plane are parallel if they do not intersect even when they are produced. Distance between the parallel lines is the same.

Transversal
A line that intersects two or more lines, at different points is called a transversal.


When a transversal intersects two lines, m and n, eight angles are formed, four angles at each point, P and Q respectively. These angles are identified 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 pairs of corresponding angles
        •  ∠1 and ∠7,  ∠2 and ∠8 are pairs of alternate exterior angles
        •  ∠4 and ∠6, ∠3 and ∠5 are pairs of alternate interior angles
        •  ∠4 and ∠5, ∠3 and ∠6 are consecutive interior angles on the same side of the transversal


Lines, Intersecting lines, . Parallel lines, Transversal, Exterior angles, Interior angles , Corresponding angles, Alternate interior angles, Consecutive Interior angles, allied interior angles , co-interior angles

If a transversal intersects two parallel lines, then
        •  each pair of corresponding angles is equal.
        •  each pair of alternate interior angles is equal.
        •  each pair of interior angles on the same side of the transversal is supplementary

Two lines intersected by a transversal are parallel if, either
        •  any one pair of corresponding angles is equal, or
        •  any one pair of alternate interior angles is equal, or
        •  any one pair of interior angles on the same side of the transversal is supplementary

Lines which are parallel to the same line are parallel to each other.

The sum of 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.

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