Question

Which describes the correct order of steps to construct an angle bisector of ∠jkl using only a straightedge and compass?

1) 1. draw a circle with a radius less than jk and center k, and label the points of intersection m and n. 2. draw a line from point m to point n. 3. draw a circle with radius mn and center m and another circle with radius mn and center n, and then draw an equilateral triangle. 4. use a straightedge to connect k to the rightmost vertex of the equilateral triangle.
2) an angle bisector cannot be constructed using only a straightedge and compass.
3) 1. draw a circle with a radius less than jk and center k, and label the points of intersection m and n. 2. draw a circle with radius mn and center m and another circle with radius mn and center n, and then draw an equilateral triangle. 3. use a straightedge to connect k to the rightmost vertex of the equilateral triangle. 4. draw a line from point m to point n.
4) 1. use a straightedge to connect k to the rightmost vertex of the equilateral triangle. 2. draw a circle with a radius less than jk and k as center, and label the points of intersection m and n. 3. draw a line from point m to point n. 4. draw a circle with radius mn and center m and another circle with radius mn and center n, and then draw an equilateral triangle.

Answer 1

The correct process for constructing an angle bisector with a straightedge and compass involves drawing a circle with center K, drawing two arcs with centers at M and N, and drawing a straight line through K and the intersection of the arcs.

Step-by-step explanation:

To construct an angle bisector of ∠jkl using only a straightedge and compass, follow these steps:

1. Draw a circle with center K and a radius less than the length of JK. Label the points where the circle intersects with the segment JK as points M and N.
2. Without changing the radius of the compass, draw two arcs with centers at M and N. These arcs will intersect at two points above and below the segment JK.
3. Draw a straight line from K through the point of intersection of the two arcs above (or below) JK. This line will bisect ∠jkl.

There is no need to construct an equilateral triangle, as that is not relevant for bisecting an angle. Therefore, the option involving the creation of an equilateral triangle is incorrect. Similarly, the options that cannot lead to creating an angle bisector and are not based on established geometric constructions should also be disregarded.