APPLIED GEOMETRY COORDINATE SYSTEM LINE CONSTRUCTION LINE CONSTRUCTION BISECTING LINE OR ARC LINE CONSTRUCTION

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1 OORDINTE SSTEM PPLIED GEOMETR ( LINE, NGLE, POLGON, R, IRLE, ND UTILITIES) LINE ONSTRUTION Z :: 2 steps are used to create one line. LINE ONSTRUTION (8.0,6.0) (2.0,2.0) Z First Step : reate two points. LINE ONSTRUTION ISETING LINE OR R L Z Second Step : Draw line between points. L3 L

2 HOW TO DIVIDE LINE INTO EQUL PRTS (ISET) Set the compass at about 2/3 the length of line. Swing an arc from point. t the same compass setting. Drawing a line from to (arc intersections) creates a line. Swing an arc from point. That is perpendicular to and bisects line. HOW TO ISET N NGLE t any radius. Swing an arc from point. 2

3 From points &. Swing two identical arcs of any radius. Z EQUL NGLES Z HOW TO DIVIDE LINE EQUL LENGTH Draw a light construction line at any convenient angle from point PROPORTIONL LENGTH 1 3 N NGLE With pencil and scale, set off from intersection of lines as many proportional divisions as need. onnect last division point to other end of line, using triangle and T-square, as shown. Proportional length 3

4 Example of Equal Parts Example of Proportional Parts HOW TO DRW POLGON SQURE HOW TO DRW SQURE Given the circle. REGULR PENTGON HEGON OTGON Draw two diameters at right angles to each other. The intersections,, are vertexes of an inscribed square. o With the T-square and 45 triangle, draw the four sides tangent to the circle. 4

5 HOW TO DRW PENTGON Given the circle. isect radius OD at O D With as center, and as radius (R), strike arc E. With as center, and E as radius (r), strike arc E. Set off distances around the circumference of the circle. Draw line and other sides. HOW TO DRW HEGON Using the compass and the radius of the circle (R), set off the six sides and connect the points with straight lines. 5

Draw vertical and horizontal center lines. o o Diagonals and D at 30 or 60 with horizontal. o o With 30 60 triangle and T-square, draw the six sides. Draw vertical and horizontal center lines.

6 Draw vertical and horizontal center lines. o o Diagonals and D at 30 or 60 with horizontal. o o With triangle and T-square, draw the six sides. Draw vertical and horizontal center lines. o o With triangle and T-square, draw the six sides tangent to the circle. HOW TO DRW OTGON o Using T-square and 45 triangle, draw the eight sides tangent to the circle. HOW TO DRW IRLE THROUGH THREE POINTS Draw lines and. Draw perpendicular bisectors EO and DO, intersecting at O. With center at O, draw required circle through the points. 6

7 HOW TO FIND THE ENTER OF IRLE Draw any horizontal chord. Draw perpendiculars from and, cutting circle at D and E D E Draw diagonals D and E whose intersection will be the center of the circle. DRWING TNGENT R IN RIGHT NGLE With given radius R, strike arc intersecting given lines at tangent points T. D E With radius R and points T as centers, strike arcs intersecting at. With as center and radius R, draw required tangent arc. DRWING TNGENT R IN N UTE NGLE Draw lines parallel to given lines, at distance R, to intersect at, the required center. 7

8 From drop perpendiculars to a given lines respectively, points T. With as center and radius R, draw required tangent arc. DRWING TNGENT R IN N OTUSE NGLE Draw lines parallel to given lines, at distance R, to intersect at, the required center. From drop perpendiculars to a given lines respectively, points T. With as center and radius R, draw required tangent arc. DRWING R TNGENT TO N R ND STRIGHT LINE Draw lines and arc parallel, respectively, to the given lines and arc at the required radius distance R, to intersect at, the required center. G + R From drop perpendiculars to a given line to obtain one point T. Draw O to locate the other point T. With center and radius R, draw required tangent arc. DRWING R TNGENT TO N R ND STRIGHT LINE Draw lines and arc parallel, respectively, to the given lines and arc at the required radius distance R, to intersect at, the required center. G - R 8

9 From drop perpendiculars to a given line to obtain one point T. Draw O to locate the other point T. With center and radius R, draw required tangent arc. DRWING R TNGENT TO TWO RS Given arcs with centers and, and required radius R. With and as centers, draw arcs parallel to given arcs and at a distance R from them; Their interaction is the center of the required tangent arc. Draw lines of centers and to locate points of tangency T, and draw required tangent arc. DRWING R TNGENT TO TWO RS Given arcs with centers and, and required radius R. With and as centers, draw arcs parallel to given arcs and at a distance R from them; Their interaction is the center of the required tangent arc. 9

10 Draw lines of centers and to locate points of tangency T, and draw required tangent arc. DRWING R TNGENT TO TWO RS ND ENLOSING ONE With and as centers, strike arcs HK r and HK R intersecting at G, the center of required tangent arc. Extended lines of G and G determine points T. DRWING R TNGENT TO TWO RS ND ENLOSING ONE With and D as centers, strike arcs HK+r and HK R intersecting at G, the center of required tangent arc. Extended lines of G and GD determine points T. 10

Constructions. Unit 9 Lesson 7

Constructions. Unit 9 Lesson 7 Constructions Unit 9 Lesson 7 CONSTRUCTIONS Students will be able to: Understand the meanings of Constructions Key Vocabulary: Constructions Tools of Constructions Basic geometric constructions CONSTRUCTIONS