1. Auxiliary Views & Development
Exploring solid geometry.

2. Construction Basics Bisecting lines Bisecting angles
Constructing 45° angles
Constructing 30° and 60° angles
Constructing Pentagons
Constructing Hexagons

3. Bisecting a line
Scribe an arc, that has a radius about 2/3 that of the line, above and below the line
Repeat the process from the other end. Join the two sets of intersecting arcs to BISECT.

4. Bisecting an Angle
From points of equal distance along each line scribe two intersecting arcs
Draw a line from the intersection of the original lines to the intersection of the arcs to BISECT the angle.

5. Dividing a line into segments
Draw a line of equal segments at any angle
Connect the end of both the original and new line together. Draw a parallel line for each segment.

6. Construct an Angle of 60°
Start with a Horizontal line segment, scribe an arc from each end using the segment length as the radius.
This creates an equilateral triangle. Three equal sides and three equal included angles. 180° ÷ 3 = 60°. Bisect this angle to create a 30° angle.

7. Construct a 45° angle
Use the Bisect a line method to obtain two perpendicular lines. Scribe an arc from their intersection.
Join the points where the arc intersects with the vertical and horizontal to form a right isosceles triangle
(Two equal sides with and included angle of 90°)

8. Construct a Hexagon
Start with an Equilateral triangle. Scribe a circle from its point to include the ends of the base line
Using the base line as a radius scribe arcs around the circle to form the points of the hexagon

9. Create a Pentagon
Start with a bisected base line

10. Auxiliary Views and Developments
Auxiliary view enable us to draw true shapes of inclined surfaces
Developments enable us to construct solid models of complex forms.

11. Auxiliary Views
Create an Auxiliary projection plane parallel to the face of the object you want the True Shape of.
Project the points of the object through the Auxiliary plane and then transfer the horizontal dimensions. TS

12. Finding True Lengths
Transfer the apparent length from the top view onto the projected height line of the Front view.
Join the ends and the resulting line is the TRUE LENGTH

13. Find the true length of the side
Development
Find the true length of the side
Apex
Mark out the development as though the Pyramid is not truncated.
Now transfer the true lengths of each edge

14. Development of a Circular Object

15. Interpenetration of Solids