Investigation 8: Geometric Construction of Bisectors
Bisecting means dividing a line segment or angle into two perfectly equal halves using a compass and straightedge. In Grade 6 Saxon Math Course 1 (Chapter 8: Advanced Topics in Geometry and Number Operations), students construct two types of bisectors. A perpendicular bisector cuts a segment exactly in half at a 90° angle. An angle bisector splits an angle into two equal smaller angles—for example, bisecting a 60° angle creates two 30° angles. The midpoint of segment XY lies on its perpendicular bisector. These constructions build precision in geometric reasoning.
Key Concepts
New Concept The word bisect means "to cut into two equal parts.".
What’s next Next, you’ll use a compass and straightedge to construct the perpendicular bisector of a segment and the bisector of an angle.
Common Questions
What does it mean to bisect a line segment or angle?
To bisect means to divide exactly in half. A bisected line segment has two equal halves; a bisected angle has two equal smaller angles.
What is a perpendicular bisector?
A line that crosses another segment exactly at its midpoint and forms a 90° angle with it. Every point on the perpendicular bisector is equidistant from the segment endpoints.
What is an angle bisector?
A ray that divides an angle into two equal parts. For example, the bisector of a 90° angle creates two 45° angles.
How do you construct a perpendicular bisector using a compass?
Open the compass to more than half the segment length. Draw arcs above and below the segment from each endpoint. Connect the two arc intersections with a straight line.
If an angle bisector divides an angle into two 35° parts, what was the original angle?
35° + 35° = 70°. The original angle measured 70°.