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he steps below describe the construction of a line AG that is parallel to segment PQ and passes through a point A outside of PQ: Step 1 shows a segment PQ with an external point A. A line drawn from A intersects PQ at a point B. Step 2 shows an arc drawn from B that intersects BQ in D and BA in E. Step 3 shows an arc drawn from Point A that intersects the segment BA extended in a point F. Which statement describes the next step?

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isobel58

Answer: Point G is obtained by using the same compass width and drawing an arc from point F, intersecting the arc drawn from A

Step-by-step explanation:

I took the test and got the right answer

The steps for constructing a parallel line require steps for constructing

angles of equal measures.

  • The statement that describes the next step is; The width of the compass is adjusted to DE and an arc is drawn from point F.

Reasons:

The steps to construct the AG parallel to PQ, passing through the point A

outside of PQ are as follows;

Step 1; A line is drawn from point A to intersect PQ at point B.

Step 2; From point B on PQ, an arc is drawn intersecting segment BQ of PQ at  D and segment BA at point E.

Step 3; To construct the angle equal to angle ∠DBE at point A, an arc is drawn from Point A with radius BD, that intersects the segment BA extended in point F

Therefore;

To construct an angle equal to the angle ∠DBE to point A, we have;

  • The width of the compass is adjusted to DE, and an arc is drawn from point F to intersect the arc drawn from point A with radius BD at point G.

The points A and G can then be joined with a straight line and extended to form the line AG.

The correct option is therefore;

  • The width of the compass is adjusted to DE and an arc is drawn from point F

Learn more about constructing a parallel line here:

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