﻿ Definition of Corresponding Angle Conjecture| Define Corresponding Angle Conjecture - Geometry - Free Math Dictionary Online

# 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.

### 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?

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

### 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°

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