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
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?
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°