Question

more constructions practice! create each construction using your compass and straight - edge. 1. construct the bisector of ∠def. 2. construct a line perpendicular to line m, through point s. 3. construct a line parallel to line r, through point a. 4. construct an angle congruent to ∠w.

Explanation:

Answer:

(1) Using a compass, with vertex \(E\) as the center, draw an arc that intersects \(ED\) and \(EF\) at two points. Then, from these two intersection - points, draw two more arcs of equal radius inside the angle. The line from \(E\) through the intersection of these two arcs is the angle - bisector of \(\angle DEF\).
(2) With \(S\) as the center, draw two arcs that intersect line \(m\) at two points. Then, from these two intersection - points, draw two more arcs of equal radius on the opposite side of \(S\) from \(m\). The line through \(S\) and the intersection of these two arcs is perpendicular to line \(m\).
(3) Through point \(A\), draw a transversal that intersects line \(r\). Then, using a compass, copy the angle formed by the transversal and line \(r\) at point \(A\) to construct a line parallel to line \(r\).
(4) Draw a ray. With the vertex \(W\) of \(\angle W\) as the center, draw an arc that intersects the two sides of \(\angle W\). Then, with the endpoint of the new ray as the center, draw an arc of the same radius. Mark the intersection of the arc and the new ray. From the two intersection - points on the sides of \(\angle W\), measure the distance between them with the compass and transfer this distance to the new arc. The ray from the endpoint of the new ray through the new intersection - point forms an angle congruent to \(\angle W\).