Principle of Geometric Construction (I) Prepared by: Asst. lecture University Of Warith Al-anbiyaa College of Engineering Bio medical Engineering Department First Class Principle of Geometric Construction (I) Prepared by: Asst. lecture Karrar Al mansoori

Angle Triangle Radius Diameter Parallel Perpendicular Square Geometric Symbols Angle Triangle Radius Diameter Parallel Perpendicular Square Centerline R , r C L

(1) Draw the line parallel to a given line and passes through a given point + C

(1) Draw the line parallel to a given line and passes through a given point + C Repeat

(2) Draw the line perpendicular to a given line at a given point Adjacent-sides method + C

(2) Draw the line perpendicular to a given line at a given point Adjacent-sides method + C Repeat

(3) Draw the line perpendicular to a given line at a given point Using Compass + C

(3) Draw the line perpendicular to a given line at a given point Using Compass r2 D r2 r1 A + C r2 > r1 B Repeat

(4) Bisect a Given Straight Line AB 1. Swing two arcs of any radius greater than half-length of the line AB with the centers at the ends of the line. 2. Join the intersection points of the arcs with a line. 3. Locate the midpoint. Given A B A B r1 r1 (not to scale)

(5) To Bisect an Angle Given 1. Swing an arc of any radius whose centers at the vertex. 2. Swing the arcs of any radius from the intersection points between the previous arc and the lines. ( r₂ greater than ½ r₁ ) 3. Draw the line. A B C Given A B C r1 (not to scale) r2 r2

Fillet and Round Round Sharp corner Fillet Round

Fillet and Round To draw the arc, we must find the location of the center of that arc. How do we find the center of the arc?

(6) To draw an arc of given radius tangent to two perpendicular lines arc radius r r r

(6) To draw an arc of given radius tangent to two perpendicular lines arc radius r center of the arc Starting point Ending point

(7) To draw an arc of given radius tangent to two lines arc radius r r r + +

(7) To draw an arc of given radius tangent to two lines arc radius r T.P.1 T.P.2

(8) To draw a line tangent to a circle at a point on the circle Given C

(9) To draw a line tangent to a circle from a point outside the circle Given mark a tangent point C