Math Problem Statement
Francis is constructing a line parallel to EF⎯⎯⎯⎯⎯ through point G.
What step should be his next step? Responses
With the compass point on G and a wider opening than was used to construct the first arc, construct an arc that intersects GD←→ and EF⎯⎯⎯⎯⎯. With the compass point on G and a wider opening than was used to construct the first arc, construct an arc that intersects G D ↔ and E F ¯ .
With the compass point on A and the same opening that was used to construct the first arc, construct an arc that intersects GD←→on the same side of point A as point G and extends to the right of point G. With the compass point on A and the same opening that was used to construct the first arc, construct an arc that intersects G D ↔ on the same side of point A as point G and extends to the right of point G .
With the compass point on G and a wider opening than was used to construct the first arc, construct an arc that intersects EF⎯⎯⎯⎯⎯ twice. With the compass point on G and a wider opening than was used to construct the first arc, construct an arc that intersects E F ¯ twice.
With the compass point on G and the same opening that was used to construct the first arc, construct an arc that intersects GD←→on the opposite side of point A and extends to the right of point G. With the compass point on G and the same opening that was used to construct the first arc, construct an arc that intersects G D ↔ on the opposite side of point A and extends to the right of point G . Segment E F and point G above segment E F. A line passes through points G and D. An arc centered at point D passes through points A and B. Point A is on line G D and point B is on segment E F.
Solution
In this scenario, it appears that Francis is attempting to construct a line through point G that is parallel to segment EF. Given that point G lies above EF and that the task involves compass constructions, Francis is likely employing a method of parallel construction using a compass and straightedge.
The steps provided refer to various ways of intersecting the segments GD and EF with arcs, which suggests that Francis is using the technique of constructing equal angles or corresponding arcs to establish a parallel line.
The correct next step, based on the information provided, is:
"With the compass point on G and a wider opening than was used to construct the first arc, construct an arc that intersects EF twice."
This step involves using a compass to create an arc from point G that intersects the line EF at two points, which is a common way to establish parallel lines through point G, ensuring that the new line will be parallel to EF.
Let me know if you'd like further clarification or details on this construction!
Here are some related questions that may help you understand the concept further:
- What is the role of the compass in constructing parallel lines?
- How can you verify that two lines are parallel after constructing them using a compass and straightedge?
- What is the significance of choosing a wider opening for the compass in this construction?
- How does the construction of parallel lines relate to the concept of corresponding angles?
- Can you use a different method, such as using a protractor, to construct parallel lines through a given point?
Tip: Always ensure your compass opening is consistent when transferring distances between points, and only adjust it when necessary to maintain the accuracy of your construction.
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Math Problem Analysis
Mathematical Concepts
Geometric Constructions
Parallel Lines
Compass and Straightedge
Formulas
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Theorems
Parallel Postulate
Corresponding Angles Theorem
Suitable Grade Level
Grades 7-9
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