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
    A. 60°, 30° and 30°
    B. 30°, 30° and 32°
    C. 58°, 32° and 32°
    D. None of the above
    Correct Answer: C


    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°

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