Question

lesson 2 practice problems

1. this diagram was created by starting with points a and b and using only straightedge and compass to construct the rest. all steps of the construction are visible. describe precisely the straightedge and compass moves required to construct the line cd in this diagram.
2. in the construction, a is the center of one circle, and b is the center of the other. identify all segments that have the same length as segment ab.

a. segment ac
b. segment ae
c. segment bc
d. segment cd
e. segment de

Explanation:

Step1: Construction of line CD

1. Place the compass at point A and set the radius to the length of AB. Draw a circle.
2. Place the compass at point B and set the radius to the length of AB. Draw a second - circle. The two circles intersect at points C and D.
3. Use the straightedge to draw the line passing through points C and D. This is the line CD.

Step2: Identifying equal - length segments

1. Since the circles are drawn with radius equal to the length of AB, any radius of these circles will have the same length as AB.

• For the circle centered at A, segments AC and AE have the same length as AB (radii of the circle centered at A).
• For the circle centered at B, segments BC and BD have the same length as AB (radii of the circle centered at B).

Answer:

1. To construct line CD: First, draw two circles with centers A and B and radius equal to AB. Then, draw a line through the intersection points C and D of the two circles using a straightedge.
2. A. segment AC, B. segment AE, C. segment BC