In geometry, the word “constructions” refers to the drawing of items such as lines, angles, and polygons using only a compass and a straightedge. The compass allows you to mark off measurements without using numbers. A straightedge is simply a ruler with no markings. Using a straightedge allows you to create straight lines and/or connect points easily. Constructions date back to the Greeks 2000 years ago. At that time, people were not proficient in arithmetic nor did their number system have fractions or decimals. This made it difficult to measure things with accuracy. Constructions provided a way to recreate the lines and angles of larger objects.
Essential Questions
- How are a compass and straightedge used to construct a line segment congruent to a given line segment?
- How are a compass and straightedge used to construct a perpendicular bisector?
- How are a compass and straightedge used to construct a line perpendicular to a given line?
Warm-Up
Think about the words congruent, bisect, parallel, and perpendicular. What do these terms mean? Before you explore constructions involving line segments and perpendicular lines, check your knowledge of these terms in this non-graded interactivity. This knowledge will help you throughout the topic. Click the player button to get started.