Question

select the correct answer from each drop - down menu. study this incomplete image of a geometric construction. this image may result from the construction of. the next step in this construction is to set the compass width to line segment bk and draw an arc centered at l intersecting the existing arc through l arc jk and draw an arc centered at l intersecting the existing arc through l line segment bk and draw an arc centered at l in the interior of the new angle. arc jk and draw an arc centered at l on the leg of the new angle

Explanation:

Step1: Recall geometric construction concepts

When constructing an angle - congruent to a given angle, we first create an arc (like arc \(JK\) in the given angle \(\angle B\)).

Step2: Determine the next step for angle - congruent construction

To construct an angle congruent to \(\angle B\) at point \(D\), after creating an arc at \(D\) (arc through \(L\)), we set the compass width to the length of arc \(JK\) (the arc that defines the opening of \(\angle B\)) and then draw an arc centered at \(L\) intersecting the existing arc through \(L\). This is based on the SSS (Side - Side - Side) congruence criterion for triangles (the two radii of the arcs and the chord of the arc).

Answer:

The first blank: an angle congruent to \(\angle B\); The second blank: arc \(JK\) and draw an arc centered at \(L\) intersecting the existing arc through \(L\)