Corresponding Angles


 
 
Concept Explanation
 

Corresponding Angles

The angles which occupy the same relative position at each intersection where a straight line crosses two others.

If the two lines are parallel, the corresponding angles are equal.

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.

Corresponding Angles Axiom: If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.

Converse of Corresponding Angles Axiom: If a transversal intersects two lines such that a pair of corresponding angles is  equal, then two lines are parallel to each other.

Corresponding Angles

Illustration: Find the corresponding angle to a, c, g and f from the figure given below :

 

Corresponding Angles

Solution:

  • Angle corresponding to "a" = "e"
  • Angle corresponding to "c" = "g"
  • Angle corresponding to "g" = "c"
  • Angle corresponding to "f" = "b"
  • Angle corresponding to "d" = "h"
  • Illustration: Prove that if a line is perpendicular to one of two given parallel lines, then it is also perpendicular to the other line.

    Solution:

    Given: PQ || RS, MN small perp PQ at the point A.

    To Prove: MN small perp PQ  at the point B.

    Proof: PQ || RS  and MN is a transversal, therefore

    small angle ABR=angle MAP                               [ Corresponding Angles]

    small Rightarrow angle ABR=90^{0}                                   small left [because angle MAP=90^{0} right ]

    small Rightarrow AB perp RS at the point B.

    Or       small MN perp RS

    Hence the proof.

    Illustration: In the given figure, BA || ED and BC || EF. Show that small angle ABC=angle DEF.

    Solution:

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    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    If two parallel lines are cut by a transversal, then the number if pairs of corresponding angles formed is ________________

    Right Option : C
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    Explanation
    Question : 2

    In the given  figure,find the values of x,y,z,when it is given that AB || CD.

    Right Option : C
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    Explanation
    Question : 3

    Find the angle correspond to Angle 7: 

    Right Option : A
    View Explanation
    Explanation
     
     
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