Mathematics Class IX

Number Systems
Polynomials
Coordinate Geometry
Lines and Angles
Triangles
Circles
Constructions
Heron’s Formula
Surface Areas and Volumes
Statistics
Probability

Parallel Lines and a Transversal

If a line passes through two distinct lines and intersects them at distant points then this line is called Transversal Line.

Here line “l” is transversal of line m and n.

Exterior Angles – and

Interior Angles – and

Pairs of angles formed when a transversal intersects two lines.

1. Corresponding Angles :

• and
• and
• and
• and

2. Alternate Interior Angles :

• and
• and

3. Alternate Exterior Angles:

• and
• and

4. Interior Angles on the same side of the transversal:

• and
• and

Transversal Axioms

1.  If a transversal intersects two parallel lines, then

• Each pair of corresponding angles will be equal.
• Each pair of alternate interior angles will be equal.
• Each pair of interior angles on the same side of the transversal will be supplementary.

2. If a transversal intersects two lines in such a way that

• Corresponding angles are equal then these two lines will be parallel to each other.
• Alternate interior angles are equal then the two lines will be parallel.
• Interior angles on the same side of the transversal are supplementary then the two lines will be parallel.

Example

Find

Solution

Here, AB ∥ CD and EH is transversal.

EFB + BFG = 180° (Linear pair)

BFG = 180° – 133°

BFG = 47°

BFG = DGH (Corresponding Angles)

DGH = 47°

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