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.

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.

$\angle XPB$ 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.

$\angle YPB = \angle YQD$

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.

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved