Geometric Construction Notes

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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 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 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 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= 2.5culture. 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.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 Sides-

Solution

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 - 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?