Example Question - corresponding angles postulate
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Geometric Proof for Parallel Line Segments
To prove \( ABCD \parallel EFG \), we look for angle relationships that would imply parallelism through the Converse of the Corresponding Angles Postulate or the Converse of the Alternate Interior Angles Theorem. The correct statement that would allow Steve to prove \( ABCD \parallel EFG \) is: \( \angle CBF \cong \angle GFC \) Using the Converse of the Alternate Interior Angles Theorem, if \( \angle CBF \cong \angle GFC \), then line segment \( ABCD \) is parallel to line segment \( EFG \).
Parallel Lines and Corresponding Angles
The given diagram shows two parallel lines, marked as "l" and "m", and a transversal that intersects these parallel lines creating corresponding angles and alternate interior angles. In the diagram, there is a 140° angle formed between the transversal and line "m." Because line "l" is parallel to line "m," the angle formed between the transversal and line "l" that corresponds to the 140° angle will also be 140°. This is due to the Corresponding Angles Postulate, which states that when a transversal crosses parallel lines, corresponding angles are equal. Since we are given the notation m // n, where "m" and "n" are lines, we can assume "n" refers to the line labeled as "l" in the diagram, meaning that "l" and "m" are parallel. With this information, we can now determine that the value of angle x is also 140°, as it is a corresponding angle to the 140° angle on line "m". Therefore, x = 140°.
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