Math Doubts

Corresponding Angles formed by Parallel Lines and their transversal

corresponding angles of transversal of parallel lines

In the case of intersection of two parallel lines by their transversal, four pairs of angles have same relative position at each intersection of every two straight lines and they are known as corresponding angles of the transversal of parallel lines.

Look at the picture, an angle has similarity in position with another angle. Each pair of such angles are corresponding angles and total four pairs of corresponding angles are possibly formed geometrically when a pair of parallel lines are intersected by their transversal line.

Property

The corresponding angles which have relative position are equal when two parallel lines are cut by their transversal and the property can be proved geometrically.

equal corresponding angles of transversal of parallel lines

$\angle XPB$ and $\angle XQD$ are two angles and they are relatively similar. Therefore, they both are called as corresponding angles. The two corresponding angles are equal geometrically when two parallel lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are intersected by their transversal $\overleftrightarrow{XY}$.

$\angle XPB = \angle XQD$

Similarly, the corresponding angles $\angle YPB$ and $\angle YQD$ are also equal geometrically.

$\angle YPB = \angle YQD$

equality corresponding angles of transversal of parallel lines

The corresponding angles $\angle YQC$ and $\angle YPA$ are equal because of similarity in position.

$\angle YQC = \angle YPA$

Finally, the pair of corresponding angles $\angle XQC$ and $\angle XPA$ are also equal.

$\angle XQC = \angle XPA$

Therefore, the animation tutorial has proved that each pair of corresponding angles are equal geometrically when two parallel lines are cut by their transversal line.



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