Geometric Construction Notes Click on the title to view a tutorial Geometric Construction Introduction • Based on principles of pure geometry and may be applied to any shape regardless of the size. • CAD is based on geometric construction so understanding geometric construction makes understanding how CAD tools work easier and increases proficiency. Background- Euclid Euclidian Geometry was developed by a Roman citizen named Euclid. Euclid lived from approx. 330 to 260bc in Alexandria, Egypt and wrote a 13 volume book called Elements which illustrated all the concepts used in Geometric Construction Background- Why Didn’t He Just Use a Ruler The Greeks could not do arithmetic because: 1. They had only positive whole numbers represented by Roman numerals (I, II, III, IV, V) - no negative numbers - no fractions or decimals -no zero Background- Why Didn’t He Just Use a Ruler So if the line were any length other than an even answer it could not be solved in Roman culture. Example: 5 / 2= 2.5 2. Had no measurement system with units so a line could not be measured. As a result they had to use other tools such as a compass and straight edge. Drawing Guidelines • Draw constructions very lightly using guidelines. • Do NOT erase your guidelines- show your work. • Only trace over the final solution NOT the construction. Safe-T Compass Review- Parts Safe-T Compass Review- Procedure Draw a Perpendicular Bisector to a Given Line Draw a Perpendicular Bisector to a Given Line Draw a Perpendicular Bisector to a Given Line- Solution Summarize the Steps in Your Own Words Bisect an Arc Summarize the Steps in Your Own Words Bisect Angle Bisect Angle Bisect Angle Bisect Angle- Solution Summarize the Steps in Your Own Words Transfer an Angle Transfer an Angle Transfer an Angle Transfer an Angle Transfer an Angle Transfer an Angle Transfer an Angle-Solution Summarize the Steps in Your Own Words Construct a Triangle Given 3 Sides Construct a Triangle Given 3 Sides Construct a Triangle Given 3 Sides Construct a Triangle Given 3 Sides Construct a Triangle Given 3 Sides Construct a Triangle Given 3 SidesSolution Summarize the Steps in Your Own Words Construct an Equilateral Triangle Given 1 Side Construct an Equilateral Triangle Given 1 Side Construct an Equilateral Triangle Given 1 Side Construct an Equilateral Triangle Given 1 Side- Solution Summarize the Steps in Your Own Words Summary Identify how the exercises relate to one another: - What do you learn from bisecting a line that you can apply to bisecting an arc? - How do you use what you learned from bisecting an arc to bisect an angle - How do the skills learned from bisecting an angle help you to transfer an angle?
