Definition of corresponding angles being elaborated:In its simplest form, corresponding angles definition is given by the angles that are formed on same side when a line cuts two other lines as shown below.
Here angles formed by lines o & a and o & b are corresponding angles provided that they are on the same side of o. It is possible that angle made by o on the bottom side of a correspond to that made by b on both the directions.
Brief on corresponding angles postulate:
According to the corresponding angles postulate, the corresponding angles are equal if two parallel lines are being cut by a transversal. If we go to above diagram, angles formed by o & a is equal to that formed by o & b.
Brief on corresponding angles theorem:
Corresponding angles theorem provides converse results to that of the postulate given above. i.e. if the corresponding angles formed by a transversal cutting two lines are equal, than the two lines are parallel to each other. Here since the two angles are corresponding, we have lines a and b as parallel.
Some important examples of corresponding angles:
Now lets go through some of the important examples of corresponding angles that makes the picture clear.
(1) When a transversal cuts two lines, how many pairs of corresponding angles can you form?
Clearly it can be seen that there are 4 pairs of corresponding angles, 2 pairs(above a & b and below a & b) on each left and right sides respectively.
(2) If ∠oa and ∠ob are formed by line o cutting parallel lines a and b, find ∠oa if ∠ob = 120° ?
From the definition of corresponding angles, if line o cuts two parallel line a and b, ∠oa and ∠ob are corresponding angles and since the two lines are parallel, they need to be equal. Hence summarizing both concepts, ∠oa = ∠ob i.e. ∠oa = 120°.
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