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Essential Question. For which of the theorems involving parallel lines and transversals is the converse true? Exploring Converses. Work with a partner. Write the converse of each conditional statement. Draw a diagram to represent the converse. Determine whether the converse is true. Justify your conclusion.
Learn how to solve proofs involving parallel lines, and see examples that walk through sample problems step-by-step for you to improve your geometry proof-writing skills.
This geometry video tutorial explains how to prove parallel lines using two column proofs. This video contains plenty of examples and practice problems for ...
If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. To show that congruent exterior angles will also prove the lines parallel, we will establish a connection between the exterior angles and angles 1 and 2, which are inside the triangles.
In advanced geometry lessons, students learn how to prove lines are parallel. More specifically, they learn how to identify properties for parallel lines and transversals and become fluent in constructing proofs that involve two lines parallel or not, that are cut by a transversal.
Two lines are parallel if they do not meet, no matter how far they are extended. The symbol for parallel is \(||\). In Figure \(\PageIndex{1}\), \(\stackrel{\leftrightarrow}{A B}\) \(||\) \(\stackrel{\leftrightarrow}{C D}\). The arrow marks are used to indicate the lines are parallel.
In geometric proofs involving parallel lines, the Corresponding Angles Postulate asserts that corresponding angles formed by a transversal intersecting two parallel lines are congruent. Similarly, the Alternate Interior Angles Theorem states that alternate interior angles are also congruent.
