
How do you prove corresponding angles are equal?
Answer
479.1k+ views
Hint: First, draw two parallel lines and a transverse intersecting them and name all the points. Then observe and find the pairs of corresponding angles present in the diagram. Recall the other properties like alternate exterior angle property and vertically opposite angle property and relate them to each other to prove one pair of corresponding angles equal.
Complete step-by-step answer:
(i)
As we know that, corresponding angles are any pair of angles each of which is on the same side of one of two parallel lines cut by a transversal and on the same side of transversal.
Here, the pairs of corresponding angles are:
and
and
and
and
We have to prove one of these pairs equal. So,
To prove:
(ii)
As we know that line segment is parallel to the line segment i.e., . We also know that the pair of angles which lie on the outer side of the two parallel lines but on either side of the transversal line are equal and are called alternate exterior angles.
So, by alternate exterior angle property,
(iii)
We also know that the angles opposite to each other when two lines intersect are equal to each other and are called vertically opposite angle.
So, by vertically opposite angle property,
(iv)
As we know that, for any numbers if and then . This property is called the transitive property of equality.
Since we get,
And,
So, by transitive property of equality, we get:
Hence, proved.
Note: We could also prove this question by using alternate interior angle property to prove as they are in the interior side and on the either side of the transversal line and then subtracting both of these angles from to obtain on LHS and on the RHS by supplementary angles property.
Complete step-by-step answer:

(i)
As we know that, corresponding angles are any pair of angles each of which is on the same side of one of two parallel lines cut by a transversal and on the same side of transversal.
Here, the pairs of corresponding angles are:
We have to prove one of these pairs equal. So,
To prove:
(ii)
As we know that line segment
So, by alternate exterior angle property,
(iii)
We also know that the angles opposite to each other when two lines intersect are equal to each other and are called vertically opposite angle.
So, by vertically opposite angle property,
(iv)
As we know that, for any numbers
Since we get,
And,
So, by transitive property of equality, we get:
Hence, proved.
Note: We could also prove this question by using alternate interior angle property to prove
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