Question

1. this diagram is a straightedge and compass construction of the bisector of angle bac. only angle bac is given. explain the steps of the construction in order. include a step for each new circle, line, and point. (from unit 1, lesson 5.)

Explanation:

Step1: Set compass at A

Place the compass at vertex A of angle BAC. Draw a circle that intersects rays AB and AC at points B and D respectively.

Step2: Set compass at B

Without changing the compass - width, place the compass at point B and draw a circle.

Step3: Set compass at D

Place the compass at point D and draw a circle with the same radius as in the previous step. Let the two circles (centered at B and D) intersect at point E.

Step4: Draw the bisector

Use the straightedge to draw a line from point A through point E. The line AE is the angle - bisector of angle BAC.

Answer:

The steps to construct the bisector of angle BAC are: 1. With the compass at A, draw a circle intersecting AB and AC at B and D. 2. With the compass at B, draw a circle. 3. With the compass at D, draw a circle intersecting the previous circle at E. 4. Draw the line AE which is the angle - bisector.