Question 1: Construct the perpendicular bisector of a line segment of length 6 cm. Show all steps.

Answer: Line bisected with perpendicular line through midpoint

Question 2: Using a compass, draw a line segment of your choice and bisect it. Verify the bisected point is equidistant from both ends.

Answer: Equidistant from both endpoints

Question 3: What is the key property of a perpendicular bisector related to a circle?

Answer: It is the set of points equidistant from the two endpoints

Question 1: Construct a triangle with side lengths 5 cm, 7 cm, and 8 cm. Then, construct the perpendicular bisector of the longest side. Explain why this bisector passes through the circumcenter.

Answer: The bisector passes through the circumcenter because it is equidistant from all vertices

Question 2: A student attempted to bisect a line segment but drew the perpendicular line outside the segment. Identify the mistake and describe how to correct it.

Answer: The perpendicular bisector should pass through the midpoint; the student must adjust the perpendicular line to cross exactly at the midpoint

Question 1: A park planner wants to install a circular fountain at the center equidistant from two park entrances located 10 meters apart. Describe how to use compass construction to find the ideal location for the fountain.

Answer: Construct perpendicular bisector of the line between entrances; the intersection is the fountain location

Question 1: Construct the perpendicular bisector of a line segment with endpoints at coordinates (2,3) and (8,7). Use the grid to find the exact intersection point.

Answer: Midpoint at (5, 5), bisector passes through (5, 5)

Question 2: Explain a common mistake students make when constructing perpendicular bisectors and how to avoid it.

Answer: Not crossing exactly at the midpoint; ensure compass points are equal and arcs intersect precisely

Question 1: A student drew a perpendicular bisector that does not pass through the midpoint of the segment. What mistake did they likely make? How can it be fixed?

Answer: They did not draw the arcs correctly to mark the midpoint; redo the arcs ensuring they intersect at the midpoint

Question 2: Construct a line segment and its perpendicular bisector. The bisector appears longer than the segment. Identify the error and correct it.

Answer: The perpendicular bisector should only cross the segment at the midpoint; check and redraw the arcs and line