Transversal

Transversal

Transversal

In geometry, a transversal is a line which cuts two or more lines at distinct points. In the figure given below, lines AB and CD are cut by the line EF at the points G and H respectively. So, EF is a transversal.
EF is a transversal

Types of angles formed by a transversal

When two line segments are cut by a transversal then there will form 8 angles. In the figure given above, transversal EF has cut the line segments AB and CD at points G and H respectively. The angles formed there are AGE, BGE, AGH, BGH, GHC, GHD, CHF and DHF.
Types of angles formed by a transversal
Interior angles: The angles formed inside the two line segments are called interior angles. In the given figure, angles AGH, BGH, GHC and GHD are interior angles.

Exterior angles: The angles formed outside the two line segments are called exterior angles. In the given figure, angles AGE, BGE, CHF and DHF are exterior angles.

Alternate angles

A pair of non adjacent interior angles on the opposite sides of a transversal is called alternate angles
Alternate angles
In the figure the alternate angles are:
i.      AGH and GHD
ii.    BGH and GHC
Note: When the two lines cut by transversal are parallel, then alternate angles are equal.

Corresponding angles

In a pair of non-adjacent angles on the same side of a transversal, one is external and other internal are called corresponding angles. 
Corresponding angles
In the figure the corresponding angles are:
i.      AGE and GHC
ii.    AGH and CHF
iii.   BGE and GHD
iv.   BGH and DHF
Note: When the two lines cut by transversal are parallel, then corresponding angles are equal.

Co-interior angles

A pair of two interior angles on the same side of a transversal are called co-interior angles. 
Co-interior angles
In the figure the co-interior angles are:
i.      AGH and GHC
ii.     BGH and GHD
Note: When the two lines cut by transversal are parallel, then co-interior angles are supplementary i.e. their sum is 180°.

Workout Examples

Example 1: Find the values of a, b, c and d from the given figure.
Example 1
Solution: Here,
                         5a + 30° + 3a – 10° = 180° ----------------> sum of co-interior angles
                or,     8a + 20° = 180°
                or,     8a = 180° - 20°
                or,     a = 160°/8
                or,     a = 20°

                         b = 5a + 30° --------------------> Corresponding angles
                            = 5×20° + 30°
                            = 100° + 30°
                            = 130°

                         c = 3a – 10° --------------------> Alternate angles
                            = 3×20° – 10° 
                            = 60° – 10°
                            = 50°

                         d = c ----------------------> Vertically opposite angles
                            = 50°

                  a = 20°, b = 130°, c = 50° and d = 50°


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