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
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?
Choices: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°