Question

4 practice 4 (from unit 1, lesson 6) priya wants to construct a line parallel to line ℓ through point c. the diagram shows the first few steps of her construction. what was the purpose of the steps shown, and what might be her next step?

Explanation:

The steps shown create congruent angles which are used to construct a parallel line. The arcs with centers at points on line $\ell$ and passing through point $C$ help in creating equal - angle relationships. The next step would be to use the points of intersection of the arcs (such as $R$ and $S$) to draw a line through point $C$. This new line will be parallel to line $\ell$ because corresponding or alternate - interior angles will be congruent.

Answer:

The purpose of the steps shown is to create congruent angles that will be used to construct a parallel line. The next step is to draw a line through point $C$ using the intersection points of the arcs (e.g., points $R$ and $S$) to ensure the new line is parallel to line $\ell$.