Corresponding Angle Conjecture

Definition of Corresponding Angle Conjecture

If two parallel lines are cut by a transversal, then the Corresponding Angles are congruent.

More About Corresponding Angle Conjecture

    If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel.

Video Examples: Corresponding Angles


Example of Corresponding Angle Conjecture

      EXAMPLE OF Converging Lines
    In the above figure, CG||DH and AF is the transversal cutting the two parallel lines. The pairs of corresponding angles ?ABC and ?BED, ?CBE and ?DEF, ?ABG and ?BEH, and ?GBE and ?HEF are equal.

Solved Example on Corresponding Angle Conjecture

Ques: l and m are parallel lines in the figure. What are the measures of ?x, ?y, and ?z?

    example of  Corresponding Angle Conjecture
    Choices:
    A. 60, 30 and 30
    B. 30, 30 and 32
    C. 58, 32 and 32
    D. None of the above
    Correct Answer: C

Solution:

    Step 1: From the figure, ?x and 58, ?y and ?z form corresponding angles.
    Step 2: ?x = 58 [Corresponding angles are equal.]
    Step 3: ?z + 90 + 58 = 180
    Step 4: So, ?z + 148 = 180
    Step 5: ?z = 180 - 148 = 32
    Step 6: ?z = ?y [Corresponding angles are equal.]
    Step 7: ?y = 32