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Geometric Constructions
Geometric Constructions
Geometric Constructions
All traditional drawing and CAD drawing techniques are based on
the construction of basic geometric elements.
A point, line, arc, and circle are the basic elements used to create
most complex drawings.
Geometric Constructions
The geometry of drawing is the same for traditional drawing and
CAD drawing.
Pure geometry problems may be solved with only the compass and
a straightedge.
Geometric Constructions
Points and Lines
A point represents a
location in space.
A line is the shortest
distance between two
points.
Geometric Constructions
Angles
An angle is formed by
two intersecting lines.
Geometric Constructions
Triangles
A triangle is a plane
figure bounded by three
straight sides.
The sum of the interior
angles is always 180º.
Geometric Constructions
Quadrilaterals
A quadrilateral is a plane figure bounded by four straight sides.
If the opposite sides are parallel, the quadrilateral is also a parallelogram.
Geometric Constructions
Polygons
A Polygon is any plane figure bounded by straight sides.
If the polygon has equal angles and equal sides it can be inscribed in or circumscribed around
a circle and is called a regular polygon.
Geometric Constructions
Circles and Arcs
A circle is a closed curve, all points of which are the same distance from a point called the
center.
Geometric Constructions
Solids
Solids bounded by
plane surfaces are
called polyhedra.
The surfaces are
called faces.
If the faces are equal
regular polygons the
solids are called
regular polyhedra.
Geometric Constructions
Bisecting a line or circular arc
Given the line or arc (AB) to be bisected.
From (A) and (B) draw equal arcs with radius
greater than half of (AB).
Join the intersections (D) and (E) with a straight
line to locate center (C).
Geometric Constructions
Bisecting an angle
Given the angle (BAC) to be bisected.
Strike the large arc (R) at any convenient radius.
Strike equal arcs (r) with a radius slightly larger than half (BC) to intersect at (D).
Draw line (AD) which bisects the angle.
Geometric Constructions
Transferring an angle
Given the angle (BAC) to be transferred to the new position at (A’B’).
Use any convenient radius (R) and strike arcs from centers (A) and (A’).
Strike equal arcs (r) and draw side (A’C’).
Geometric Constructions
Drawing a line parallel to a line at a given distance
Given the line (AB) and the distance (CD)
Draw two arcs at (E) and (F) with a radius equal to (CD).
Draw the line (GH) tangent to the two arcs.
Geometric Constructions
Dividing a line into equal parts
Given the line to be divided
Draw a light construction line at any convenient angle from one end of the given line.
With dividers or scale, set off from the intersections of the lines as many equal divisions as needed
(in this example, three).
Connect the last division point to the other end of the given line using a triangle and T-square.
Slide the triangle along the T-square and draw parallel lines through the other division points.
Geometric Constructions
Drawing a Square
Given the inscribed circle, draw two diameters at
right angles to each other. The intersections of
these diameters with the circle are the vertexes of
an inscribed square.
Given the circumscribed circle, use the T-square
and 45º triangle and draw the four sides tangent
to the circle.
Geometric Constructions
Drawing a Hexagon
Given the inscribed circle, draw vertical and horizontal center lines and the diagonals (AB) and
(CD) at 30º or 60º with the horizontal.
With the 30º x 60º triangle and T-square, draw the six sides of the hexagon.
Given the circumscribed circle, draw vertical and horizontal center lines .
With the 30º x 60º triangle and T-square, draw the six sides of the hexagon tangent to the circle.
Geometric Constructions
Drawing an Arc Tangent to a Line and Through a Point
Given line (AB), point (P), and radius (R)
Draw line (DE) parallel to the given line (AB) at the distance
(R) from it.
From point (P) draw an arc with a radius (R) intersecting line
(DE) at point (C).
From point (C) draw the arc tangent to line (AB) and through
point (P).
Geometric Constructions
Drawing an Arc Tangent to Two Lines at Acute or Obtuse Angles
Given two intersecting lines not making a 90º angle and the distance (R)
Draw lines parallel to the given lines at a distance (R) from them to intersect at point (C).
With (C) as the center and with the given radius (R) draw the required tangent arcs between the
given lines.
Geometric Constructions
Drawing an Arc Tangent an Arc and a Straight Line
Given the straight line (AB) and the arc with radius (G) and the distance (R)
Draw a line parallel to the given lines at the distance (R).
Draw an arc from center (O) with a radius equal to (G) plus (R) to intersect at (C).
With (C) as the center and with the given radius (R) draw the required arc at the given radius (R)
and tangent to the given line and arc.
Geometric Constructions
Drawing an Arc Tangent to Two Arcs
Given the two arcs with centers (A) and (B) and the distance (R)
With (A) and (B) as centers draw arcs parallel to the given arcs at the distance (R) from them to
locate the intersection (C).
With (C) as the center draw the required tangent arc at the given radius (R) to the given arcs.