Math Problem Statement
Solution
The problem asks to determine which lines are parallel if ∠3 and ∠5 are congruent, and the diagram shows two transversal lines crossing a set of four lines labeled a, b, c, and d.
Given that ∠3 and ∠5 are congruent, they are corresponding angles formed by a transversal cutting through two parallel lines. According to the corresponding angles postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines must be parallel.
Here, lines c and d are cut by the transversal, and angles 3 and 5 are corresponding angles. Therefore, lines c and d must be parallel.
Thus, the correct answer is A) c // d.
Would you like further explanation or more details?
Here are 5 related questions you might want to explore:
- What are alternate interior angles and how do they relate to parallel lines?
- How do you prove that two lines are parallel using the transversal angle relationships?
- What are supplementary angles, and how are they involved in parallel line theory?
- How can the angle sum property be used to explore transversals?
- How can we apply parallel line properties in geometric proofs?
Tip: When working with transversals, always check for angle congruency or supplementarity, as these are key to proving parallel lines.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversals
Angle Congruence
Formulas
Corresponding Angles Postulate
Theorems
Corresponding Angles Theorem
Suitable Grade Level
Grade 8-10
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