Corresponding Angles Axiom

Corresponding angles are formed when a given transversal line crosses two parallel lines. In the event that the corresponding angles are congruent, these angles can be used to determine the degrees of the other angles of the parallel lines. Corresponding angles are a pair of nonadjacent angles, one interior, and one exterior, both on the same side of the transversal. If two lines are parallel and cut by a transversal then the pair of corresponding angles are equal.
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Corresponding angles axiom:

Angles in the same position. In the given figure PQ is a straight line and RS is a straight line. The lines PQ and RS are parallel to each other. And TU is a line which cuts the parallel lines ( PQ and RS) so the line TU is called as transversal line. A straight line cutting each of two other co planar straight lines at different points. Is known as a transversal line.

There are eight angles present in the figure. The eight angles are a , b , c , d , e , f , g , h. Among these eight angles the corresponding angles are  ( a , e ) ( b , f ) ( c , g ) ( d , h ) so angle a = angle e, angle b = angle f, angle c = angle g and angle d = angle h.
Parallel lines cut by transversal
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Example problem for corresponding angles axiom:

1) By using corresponding angles axiom find missing angles in the given figure?
corresponding angles
Solution:

we have to find the missing angles
The missing angles are a, b, x, y. Here a transversal line crosses two parallel lines. Therefore, the angles are corresponding angles.
By using the Corresponding angles axiom we can find the missing angles.

Angle 45 = x

So the missing angle x is 45o

Angle 135 = Angle a

So the missing angle a = 135o

Angle 135 = angle b

So the missing angle b = 135o

Angle 45 = angle y

So the missing angle y = 45o
Thus we found the missing angles using Corresponding angles axiom

My forthcoming post is on how do you evaluate an algebraic expression and cbse syllabus for class 9 will give you more understanding about Algebra.