Geometric Construction

1. Geometric Construction Stephen A. Jung Sierra College

2. Points and Lines • Point – represents a location in space or on a drawing • No height, width, or depth • Represented by the intersection of two lines • Short cross bar on a line, or • A small point element e.g. ( + x l ) • Line – is defines as “that which has length without width”1 • Straight Line is the shortest distance between two points • Lines can be: • Parallel – symbol = ll • Perpendicular – symbol = • Plane – is defined as: • 3 points in a space • 1 point and an entity with end points e.g. line or arc 1 Defined by Euclid

3. Angles • Angles are formed by two intersecting lines • Common symbol = a • 360 Degrees in a full circle (360o) • A degree is divided into 60 minutes (60’) • A minute is divided into 60 seconds (60”) • Example: 54o 43’ 28” is read 54 degrees, 43 minutes, and 28 seconds. • Different kinds of angles are:

4. Triangles • A triangle is a plane figure bounded by three straight lines and the sum of the interior angles is always 180o. • Types of triangles:

5. Quadrilaterals • A quadrilateral is a plane figure bounded by four straight sides. • If the opposite sides are parallel, the quadrilateral is also a parallelogram.

6. Polygons • A polygon is any plane figure bounded by straight lines. • If the polygon has equal angles and equal sides, it can be inscribedor circumscribed around a circle, an is called a regular polygon.

7. Circles and Arcs • A circle is a closed curve with all points the same distance from a point called the center. • Attributes of a circle:

8. Bisecting a Line or Arc Given line A-B or Arc A-B Compass Method B A Midpoint of line Construction circles have the same diameter and the radius is equal to more than ½ the length of the line.

9. R Bisecting an Angle Given angle A-B-C Compass Method C Equal Angles A Bisector B Initial construction circle drawn at any convenient radius. Second and third circles radius equal to first.

10. Transferring an Angle Compass Method Z’ Z Equal Angles r’ r=r’ Given Angle X-Y-Z R=R’ Equal Angles R’ r X’ Y R Y’ New Location X Second circle radius (R’) equal to first circle radius (R). Initial construction circle drawn at any convenient radius.

11. Drawing a Triangle with sides given. D E F E D E D F Measure length of each side given. Construct circles from end points of base.

12. Drawing a Right Triangle with only two sides given M N R=M R= 1/2 N M N Measure length of each side given. Construct base segment N. Construct a circle = M from one end point of base.

13. Drawing an Equilateral Triangle R R S R Given Side All angles are equal to:? 60o Measure length of side given. Draw construction circles from the end points of the given side with the radius equal to that length.

14. Drawing Regular Polygons using CAD • Required information prior to the construction of a polygon: • Number of sides • Center location • Radius of the polygon • Inscribed in a circle or Circumscribed about a circle R R Sides = 6 Sides = 6 Inscribed Circumscribed

15. Tangents

16. Drawing a Circle Tangent to a Line R Center of Circle G 90o Tangent Point Given Radius Offset Given Line

17. Drawing a Tangent to Two Circles Tangent Points C1 C2 T Tangent Points T C1 C2 T T

18. Tangent to Two Arcs or Circles Only One Tangent Point C1 C2

19. Drawing a Tangent Arc in a Right Angle • Required information prior to the construction of an Arc Tangent to a line: • Radius of the desired Arc = R Offset R R R Offset Given Right Angle

20. Drawing Tangent Arcs: Acute & Obtuse Angles Required information prior to the construction of an Arc Tangent to a line: Radius of the desired Arc = R Offset T R Offset R R Offset R T Acute Angle Acute Angle Example Offset R R Obtuse Angle T T Obtuse Angle Example

21. Arc Tangent to:an Arc and a Straight Line Offset Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = RD RG+RD Given Arc T RG Offset RD RD T Given Line

22. Arc Tangent to:an Arc and a Straight Line Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = RD Given Arc Offset RG-RD RG T Offset RD RD T Given Line

23. Arc Tangent to two Arcs Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = RD Offset Offset RG+RD RG’+RD T RG RG’ T RD Given Arcs

24. Arc Tangent to two Arcs cont. Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = RD Offset RG+RD RG Offset RG’-RD T Given Arcs RD RG’ T

25. Arc Tangent to Two Arcs cont. Enclosing Both Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = RD RD T RG’ RG T RD-RG’ RD-RG Given Arcs

26. Arc Tangent to Two Arcs & Enclosing One T Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = RD Given Arcs RD RG’ RG T RD-RG’ Offset RD+RG

27. That’s All Folks!

28. Tangent Arcs – Obtuse Angles Example

29. Tangent Arcs – Acute Angles Example

30. Circles and Arcs

31. Polygons

32. Quadrilaterals

33. Triangles

34. Angles

35. Points and Lines