This diagram is a straightedge and compass construction of a line perpendicular to line AB passing through point C.

Why was it helpful to construct point D in the perpendicular line construction through point C?

• To identify the center of the circle

• To mark the midpoint of line AB

• To be the same distance from C as A.

• To ensure the line is perpendicular to AB

Which statement is true about line EF in the given construction?

• Line EF is parallel to line CD.

• Line EF is the perpendicular bisector of segment BA.

• Line EF is the bisector of angle BAC.

This diagram is a straightedge and compass construction.

A is the center of one circle, and B is the center of the other. A rhombus is a quadrilateral with 4 congruent sides.

Why is quadrilateral ACBD a rhombus?

• AB = CD

• It has two pairs of parallel sides.

• CA = CB = DA = DB

• It has four right angles.

A, B, and C are the centers of the three circles.

Which line segment is congruent to HF?

• DF

• CD

• AB

• CB

In the construction, A is the center of one circle, and B is the center of the other.

Why is segment EA the same length as segment BC?

• Both segments are radii of the same circle or congruent circles.

• Both segments are tangents to the same point.

• Both segments are diameters of different circles.

• Both segments are chords of the same circle.

In this diagram, line segment CD is the perpendicular bisector of line segment AB. Assume the conjecture that the set of points equidistant from A and B is the perpendicular bisector of AB is true.

Is point M closer to point A, closer to point B, or the same distance from both points?

• Point M is the same distance from both points.

• Point M is closer to point B.

• Point M is not on the perpendicular bisector.

• Point M is closer to point A.

Here is a diagram of a straightedge and compass construction.

C is the center of one circle, and B is the center of the other.

Why is the length of segment CB the same as the length of segment CD?

• Both segments are radii of the same circle centered at C.

• Both segments are chords of the same circle.

• Both segments are diameters of different circles.

• Both segments are tangents to the same point.

Which of the following is true about the perpendicular bisector in the construction?

• It is a diameter of the circle.

• It is parallel to line AB.

• It is a tangent to a circle centered at A.

• It is equidistant from points A and B.