Geometric Construction

Geometric Construction Unit C BY: K. L. TATRO CENTRAL HIGH SCHOOL EAST

Points and Lines • A Pointrepresents a location in space or in a drawing and has no width, height, or depth. • A Line is defined as “that which has length without breadth.” A straight line is the shortest distance between two points. Lines Horizontal Perp Lines Indefinite Points Definite Vertical

Angles • An angle is formed by two intersecting lines. STRAIGHT ANGLE RIGHT ANGLE ACUTE ANGLE COMPLETE CIRCLE OBTUSE ANGLE COMPLEMENTARY ANGLES SUPPLEMENTARY ANGLES

Regular Polygons • MORE THAN THREE SIDE CONSTRUCTED AROUND A CIRCLE • POLYGON MAY BE INSCRIBED (POINTS TOUCH) OR CIRCUMSCRIBED (FLATS TOUCH) • ALL SIDES ARE EQUAL IN LENGTH AND IN ANGLE INSCRIBED PENTAGON SQUARE HEXAGON OCTAGON TRIANGLE CIRCUMSCRIBED

Polygons … • ANGLES IN REGULAR POLYGONS ARE FOUND BY DIVIDING A CIRCLE (3600) BY THE NUMBER OF SIDE • Except a triangle, then we use 1800 • E.g. Hexagon has 6 sides. 360/6=60. Therefore we use a 600 triangle to complete a hexagon Circumscribed Inscribed

Creating a Perpendicular Bisecting Line.. • Bisect = 2 equal parts • Perpendicular = 90o to its counterpart • From each end of the given line, draw an arc that is greater than half • Connect the two intersections from each of the created arcs

Using a ruler to divide… Dividing 6 equal spaces

Dividing a given space.. • Dividing horizontal space • Place ruler so that it touches each end at a number that you can divide. • Put dots on those points • Draw vertical lines through those dots

Dividing a given space vertically • Dividing vertical space • Place ruler so that it touches the top and bottom line at a number that you can divide. • Put dots on those points • Draw horizontal lines through those dots

Tangent Lines • A line that touches a circle or arc in a point of tangency. Is this tangent?

Creating a tangent arcs and circles Draw a line the distance of the radius away from the given line (the line we want to be tangent to) then create a circle using the radius line to mark the center of the circle radius

Creating a circle or arc to two given lines Draw a line the distance of the radius away from each given line. Where the two lines cross, that is where you will place the middle of the circle. R R

Creating a circle or arc to a line and an arc. • Create a line tangent to the given straight. • Mark the radius away from the edge of the circle you want to be tangent to. • Draw an arc from the given circle’s mid-point that represents a distance of the radius away from the edge • Draw the circle using the point of crossing as the mid-point R R

Handout: Arcs tangent to a circle and a line.

Handout: Exclusive Arcs…..

Handout: Inclusive Arcs

Homework • Worksheets • Exercise 3.14 • Figure 4.76 (handout) • Exercise 3.12

Figure 3.14 • Find center and draw the outer circle.

Figure 3.14 • Add the centerlines for the 6 circles @ 600 between each

Figure 3.14 • Draw in the 6 needed circles

Figure 3.14 • Mark lines at 150 increments • Draw teeth so that each line intersects the next at 900 Each line is at 90o to the next

Figure 3.14 • Finish with the hub and keyway • Darken final object and leave construction lines of they are light • Add border and title block

Questions? Remember that all drawings are done in a formal sketch fashion.. That means to sketch with some aides, and that there is some built in assumption of error for accuracy, but not concepts…. Earn 15 points extra credit by completing the 6 page handout out marked Chapter 5: Geometric Construction.

Geometric Construction