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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?
- m∠1 + m∠4 = 180° (correct)
- m∠1 + m∠2 = 180°
- m∠3 + m∠4 = 360°
- m∠2 + m∠4 = 90°
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?
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?
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?
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).
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?
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?
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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