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Questions and Answers
Given: AB // DC and m∠2 ≅ m∠4. Prove: AD // BC. What is the equation that justifies this?
Given: AB // DC and m∠2 ≅ m∠4. Prove: AD // BC. What is the equation that justifies this?
Which lines are parallel? Justify your answer based on angles (110,110,80).
Which lines are parallel? Justify your answer based on angles (110,110,80).
Lines a and b are parallel because their corresponding angles are congruent.
In the diagram, if g ∥ h, m∠1 = (4x + 36)°, and m∠2 = (3x - 3)°, what is the measure of ∠3?
In the diagram, if g ∥ h, m∠1 = (4x + 36)°, and m∠2 = (3x - 3)°, what is the measure of ∠3?
60
Parallel lines e and f are cut by transversal b. What is the value of x?
Parallel lines e and f are cut by transversal b. What is the value of x?
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Which diagram shows lines that must be parallel when cut by a transversal?
Which diagram shows lines that must be parallel when cut by a transversal?
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Parallel lines e and f are cut by transversal b. What is the value of y?
Parallel lines e and f are cut by transversal b. What is the value of y?
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Which lines are parallel? Justify your answer based on angles (75, 75, 115).
Which lines are parallel? Justify your answer based on angles (75, 75, 115).
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Lines c and d are parallel, cut by transversal p. What must be true by the corresponding angles theorem?
Lines c and d are parallel, cut by transversal p. What must be true by the corresponding angles theorem?
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Which equation is enough information to prove that lines m and n are parallel when cut by transversal p?
Which equation is enough information to prove that lines m and n are parallel when cut by transversal p?
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Which set of equations is enough information to prove that lines a and b are parallel when cut by transversal f?
Which set of equations is enough information to prove that lines a and b are parallel when cut by transversal f?
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Study Notes
Proving Lines Parallel
- To prove lines are parallel, analyze angle relationships formed by transversals.
- If m∠1 + m∠4 = 180°, then lines AB and DC are parallel (AB // DC).
- If corresponding angles are congruent, lines are parallel (e.g., m∠2 ≅ m∠4 implies AD // BC).
Angle Relationships and Properties
- In parallel line configurations, alternate exterior angles congruence indicates parallel lines (e.g., lines e and f confirmed as parallel due to congruent angles).
- When two lines are parallel and cut by a transversal, corresponding angles are equal (e.g., ∠2 ≅ ∠6).
Solving Angle Measures
- Given angle equations can help determine angle measures and values for variables (e.g., m∠1 = (4x + 36)° and m∠2 = (3x - 3)° leads to m∠3 = 60°).
- Example solving: If parallel lines yield x = 25, and y = 130 from angle measures formed by transversals.
Justifying Parallel Lines
- Parallel lines can be justified through congruent angle pairs (e.g., alternate interior, corresponding, or same-side interior angles).
- Various angle equations can confirm whether lines are parallel; for instance, a = d, c = d, and b + d = 180° are sufficient to prove m and n are parallel.
Identifying Parallel Lines in Diagrams
- Recognize patterns in diagrams where transversals intersect parallel lines, checking for congruent angles to assert parallelism.
- In conjunction scenarios, multiple angles being equal can signify the same conclusion (e.g., lines a and b being parallel from m∠1 = 110° and m∠3 = 70°).
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Test your understanding of proving lines parallel with these flashcards. Each card presents a scenario with angles and definitions to help you grasp the concepts better. Perfect for reinforcing your knowledge in geometry.
