AY 2024-2025- T1- Week-03- Geometric Construction-01.pptx

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1. MODULE-02: GEOMETRIC CONSTRUCTION I [ LINES + ANGLES ]

2. I. LINES 1.1. Transferring a Given Length of a Line 1.2. Bisecting a Given Line 1.3. Line Perpendicular to a Point on the Given Line 1.4. Line Perpendicular to a Given Line and Passing through a Given Point 1.5. Line passing through a point and Parallel to a Given Line 1.6. Line parallel to and at a given distance from line AB 1.7. Dividing a line into n- equal segments II. ANGLES 2.1. Transferring an Angle 2.2. Bisecting an Angle 2.3. Dividing an angle into n-equal parts ITEMS FOR DISCUSSION

3. I. LINES T he sho r test di s ta n ce between two points A set of points organized that have length and direction, but no thickness PERPENDICULAR vs PARALLEL lines 1.1 . Transferring a Given Length of a Line 1.2. Bisecting a Given Line 1.3. Line Perpendicular to a Point on the Given Line 1.4. Line Perpendicular to a Given Line and Passing though a Given Point 1.5. Line passing through a point and Parallel to a Given Line 1.6. Line parallel to and at a given distance from line AB 1.7. Dividing a line into n- equal segments II. ANGLES 2.1. Transferring an Angle 2.2. Bisecting an Angle 2.3. Dividing an angle into n-equal parts ITEMS FOR DISCUSSION

4. 1.1. Transferring a Given Length of a Line • Given: Line AB A B

5. 1.2. Bisecting a Given Line • Given: Line AB A B

6. 1.2 . Bisecting a Given Line 1. Using point A as center and radius R greater than one-half of the length of line AB , draw an arc extending to both sides of line AB . 2. Using point B as center and the same radius R, draw a second arc intersecting the first arc. Label the intersections as point C and D . 3. Draw a line connecting points C and D. Line CD bisects line AB. Line CD is called: PERPENDICULAR BISECTOR

7. 1.3. Line Perpendicular to a Point on the Given Line • Given: Line AB A B

8. 1.3. Line Perpendicular to a Point on the Given Line 1. Extend line AB beyond point B. Using point B as center and any radius R , draw an arc intersecting line AB at point C and the extension line at point D. 2. Using point C as center and any radius R greater than one-half of segment CD , draw an arc extending to both sides of segment CD.

9. 1.3. Line Perpendicular to a Point on the Given Line 3. Repeat the process, this time using D as center. Label the points of intersection as points E and F. 4. Connect points E and F. Line EF is perpendicular to line AB at point B.

10. • Given: Line AB and Point O. O A B 1.4. Line Perpendicular to a Given Line and Passing through a Given Point

11. 1.4. Line Perpendicular to a Given Line and Passing though a Given Point 1 . Using point O as center and any radius R greater than the distance between point O and line AB draw an arc intersecting at points C and D 2. Using point C as center and any radius R1 greater than one-half of segment CD, draw an arc on the opposite side of line AB

12. 1.4. Line Perpendicular to a Given Line and Passing though a Given Point 3. Repeat step 2m this time using point D as center. Label the point of intersection of the two arcs as F. 4. Connect points O and F. Line OF is perpendicular to line AB.

13. • Given: Line AB and Point O O A B 1.5. Line passing through a point and Parallel to a Given Line

14. 1.5. Line passing through a point and Parallel to a Given Line 1 . Using point O as center and any radius R greater than the distance from point O to line AB , draw an arc cutting line AB at point C . 2. Using point C as center and the same radius R , draw another arc passing through point O and cutting line AB at point D.

15. 1.5. Line passing through a point and Parallel to a Given Line 3. Using point C again as center and distance OD as radius , draw a third arc intersecting the first arc. Label the intersection as F. 4. Connect points O and F. Line OF is parallel to line AB.

16. • Given: Line AB and Distance L S A B 1.6. Line parallel to and at a given distance from line AB

17. 1.6. Line parallel to and at a given distance from line AB Using point A as center and the given distance S as radius, draw an arc on one side of line AB. Label the first arc as 1. Using point B as center and the same radius, draw a second arc. Label this arc 2. Extend line AB beyond points A and B. Using point A as center and any radius R, draw an arc cutting line AB at point C and the extension line at point D .

18. 1.6. Line parallel to and at a given distance from line AB 4 . Using point C (first) and point D (second) as centers and any radius R1 in both operations, draw two arcs on both sides of line AB. Connect the two intersections. Note that the line intersects arc 1. Label the point of the intersection as point E. 5 . Repeat steps 3 and 4. This time using B as center. Label the point of the line and arc 2 as point H. 6.Connect points E and H. Line is parallel to line AB at a distance.

19. 1.7. Dividing a line into n- equal segments • Given: Line segments. N= 3 AB and the number of A B

20. 1.7. Dividing a line into n- equal segments Using point A as origin draw another line CD making an angle of 30-45 degrees with line A B. Starting from point A and using any convenient length. Layout points n on line CD at equal distances. Draw a line connecting point B and point 1

21. 1.7. Dividing a line into n- equal segments 4. Draw a fourth line parallel to line 1 B passing point 2. (Recall steps in making line parallel to a given line-passing through a given point). Label points of intersection of Line AB as E 5. Repeat Step 4. 6. Line AB is now divided into n equal parts.

22. I. LINES 1.1 . Transferring a Given Length of a Line 1.2. Bisecting a Given Line 1.3. Line Perpendicular to a Point on the Given Line 1.4. Line Perpendicular to a Given Line and Passing though a Given Point 1.5. Line passing through a point and Parallel to a Given Line 1.6. Line parallel to and at a given distance from line AB 1.7. Dividing a line into n- equal segments II. ANGLES are formed when two straight lines or rays meet at a common endpoint 2.1. Transferring an Angle 2.2. Bisecting an Angle 2.3. Dividing an angle into n-equal parts ITEMS FOR DISCUSSION

23. • Given: Angle ABC A Ɵ B C 1.8. Transferring an Angle

24. 2.1. Transferring an Angle Layout line BC in the new position/ location. Label it line B’C’. 2. Using point B as center and any radius R, draw an arc intersecting rays BA and BC at points D and E respectively. 3. Without changing the opening of your compass and using B’ as center, draw an arc intersecting ray B’C’ at point D’.

25. 2.1. Transferring an Angle 4. Using point D’ as center and the distance from points D and E as radius, draw an arc intersecting the first arc and at point A’. 5. The line connecting point B’ to A’ forms the given angle ABC in the new position as angle A’B’C’.

26. • Given: Angle ABC A Ɵ B C 2.2. Bisecting an Angle

27. 2.2. Bisecting an Angle 1. Using point B as center and any radius R, draw an arc intersecting ray AB and ray BC at points D and E respectively. 2. Using point D as center and any radius R1, draw a second arc away a from point B and between side BA and BC. 3. Using the same radius R1 and E as center, draw a third arc that intersects the second arc at point F. 4. Connect points B and F. Line BF bisects angle ABC at two equal parts. Line BF is called: Angle Bisector C

28. • Given: Angle N=3 ABC and N. A Ɵ B C 2.3. Dividing an angle into n-equal parts

29. 2.3. Dividing an angle into n-equal parts 1. Using point B as center and radius R, draw an arc intersecting ray BA and ray BC at points C and D respectively. 2. Connecting point D to E, divide the resulting chordline into n equal segments. 3. Label the n-1 new points on the chord DE. Connect the designated points to point B. 4. The line divide angle ABC into n-equal parts C

30. PLATE #02 Title: Geometric Construction I 1. Answer the given problem set using the concepts and principles discussed. 2. Use “H” pencil. 3. Write your name (Surname, First Name M.I.), section (CIV2XX), instructor (Ar. Carl Carulla), and title (Geometric Construction I)at the back of your paper. Use a text height of 0.3cm.

31. PLATE #02 Title: Geometric Construction I

32. Super thank you! 