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Geometric Constructions

geometrical contraction

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geometrical contraction for engineering graphics students for first year students

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  • Geometric Constructions

  • Points and LinesA point represents a location in space.A line is the shortest distance between two points.

  • AnglesAn angle is formed by two intersecting lines.

  • TrianglesA triangle is a plane figure bounded by three straight sides.The sum of the interior angles is always 180.

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

  • PolygonsA 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.

  • Circles and ArcsA circle is a closed curve, all points of which are the same distance from a point called the center.

  • SolidsSolids 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.

  • Bisecting a line or circular arcGiven 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).

  • Bisecting an angleGiven 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.

  • Transferring an angleGiven the angle (BAC) to be transferred to the new position at (AB).Use any convenient radius (R) and strike arcs from centers (A) and (A).Strike equal arcs (r) and draw side (AC).

  • Drawing a line parallel to a line at a given distanceGiven 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.

  • Dividing a line into equal partsGiven the line to be dividedDraw 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.

  • Drawing a SquareGiven 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 45 triangle and draw the four sides tangent to the circle.

  • Drawing a HexagonGiven the inscribed circle, draw vertical and horizontal center lines and the diagonals (AB) and (CD) at 30 or 60 with the horizontal. With the 30 x 60 triangle and T-square, draw the six sides of the hexagon.Given the circumscribed circle, draw vertical and horizontal center lines .With the 30 x 60 triangle and T-square, draw the six sides of the hexagon tangent to the circle.

  • Drawing an Arc Tangent to a Line and Through a PointGiven 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).

  • Drawing an Arc Tangent to Two Lines at Acute or Obtuse AnglesGiven two intersecting lines not making a 90 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.

  • Drawing an Arc Tangent an Arc and a Straight LineGiven 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.

  • Drawing an Arc Tangent to Two ArcsGiven 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.