Overview
This lecture covers fundamental geometric constructions using a compass and straightedge, emphasizing construction steps and important properties.
Tools for Constructions
- A compass is used for drawing circles and transferring distances.
- A straightedge is used for drawing straight lines but does not measure length.
Constructing a Congruent Segment
- To copy a segment, measure its length with a compass and mark that length from a new point using the same compass width.
Constructing a Congruent Angle
- To copy an angle, draw an arc across the given angle's arms, replicate the arc from a new point, and use the compass to measure and mark the arc's width on the new arc.
Constructing the Perpendicular Bisector of a Segment
- Place the compass on one endpoint and draw an arc above and below the segment.
- Without changing the compass width, repeat from the other endpoint.
- Draw a straight line connecting intersection points of the arcs to bisect the segment perpendicularly.
Constructing an Angle Bisector
- Draw an arc across both sides of the angle.
- From each intersection on the arms, draw arcs inside the angle so they intersect.
- Draw a straight line from the vertex through the intersection of the arcs to bisect the angle.
Key Terms & Definitions
- Compass — a tool for drawing circles/arcs and copying distances.
- Straightedge — a tool for drawing straight lines, without measuring.
- Bisector — a line that divides a segment or angle into two equal parts.
- Perpendicular — two lines that intersect at a 90-degree angle.
Action Items / Next Steps
- Practice each construction (segment copy, angle copy, perpendicular bisector, angle bisector) with compass and straightedge.
- Review geometric construction vocabulary.