Which figure appears to contain all the characteristics above?
Understand the Problem
The question is asking which geometric figure out of the provided options satisfies all the given characteristics about parallel lines, transversals, and angle relationships.
Answer
D
Answer for screen readers
The correct figure is D.
Steps to Solve
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Identify the Parallel Lines and Transversal First, note that lines $j$ and $k$ are parallel, and line $t$ is the transversal that intersects these parallel lines.
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Analyze Angle Relationships Next, apply the properties of angles formed when a transversal crosses parallel lines:
- Angles on the same side of the transversal are supplementary. For instance, Angle 2 + Angle 3 = $180^\circ$.
- Alternate interior angles are equal. So, Angle 2 = Angle 4 and Angle 5 = Angle 7.
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Compare Each Figure's Angles Now, compare the angle relationships noted with the angles in each figure:
- In option A: Check if Angle 2 = Angle 4 and Angle 5 = Angle 7.
- In option B: Check the same angle relationships.
- In option C: Check the same angle relationships.
- In option D: Check the same angle relationships.
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Identify the Correct Figure Finally, identify which figure satisfies all the conditions, ensuring Angle 2 matches Angle 4 and Angle 5 matches Angle 7.
The correct figure is D.
More Information
Figure D illustrates the parallel lines $j$ and $k$ intersected by the transversal $t$, with angles respecting the relationships outlined in the problem statement.
Tips
- Overlooking Angle Types: Sometimes students may forget which angles are alternate interior versus corresponding. It’s important to specifically identify the types of angles involved in the relationships.
- Misreading Angle Labels: Ensure to reference the correct angle numbers when comparing properties.
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