This diagram is a straightedge and compass construction. C is the center of both circles.

Select all statements that must be true by construction.

• Segments AB and AD have the same length.

• Segments AC and AD have the same length

• Segments AC and CD have the same length.

• Triangle BCE is isosceles.

• Triangle CDE is isosceles

Line CD is the perpendicular bisector of segment AB. The lines intersect at point E. Which of these statements is true?

• E is closer to A.

• E is closer to B.

• E is the same distance from A and B.

• There is not enough information to be sure.

Choose a description you can be sure is accurate for the shape she constructed.

• 2 congruent sides, but not all 4

• 4 congruent angles

• 4 congruent sides

• 4 congruent sides and 4 congruent angles

What is the definition of a circle?

Fill in the blanks using the available answer choices:

altitude

median

perpendicular bisector

The included image shows the result of using straightedge and compass tools to construct the ______ for segment AB.

Han followed these instructions to make the image.

1. Given line j, mark two points on the line.

2. Construct congruent circles a and b centered at the points on j.

3. Construct line g through the intersection points of a and b.

4. Construct circle c centered at one intersection point of a and b. Mark the two intersection points of c and g.

5. Construct congruent circles h and k centered at the points on g.

6. Construct line i through the intersection points of h and k.

Select all the true statements about each pair of lines in this construction.

Explain why segments AB and AC have the same length.

Classify triangle ABC (what kind of triangle is this). Justify your classification.

Mai wants to construct a regular hexagon inscribed in the circle centered at C. Will these instructions work to finish the hexagon from the construction given? If so, explain why Mai is correct. If not, finish the construction correctly.

1. Draw the circle centered at D with radius CD.

2. Mark the intersection of the circle with the circle centered at C, and label that point E.

3. Draw the circle centered at E with radius DE.

4. Mark the intersection of the circle with the circle centered at D, and label that point F.

5. Connect ABCDEF to make a regular hexagon.