To construct triangle ABC:
1. Using a ruler, draw a line segment AB of length 8 cm.
2. With A as the center, draw an arc on the same side as B, intersecting AB at point C.
3. With C as the center, draw an arc to create an angle of 30 degrees. The arc should intersect the previous arc drawn at point D.
4. Connect points A and D with a straight line segment.
5. With B as the center, draw an arc on the opposite side, intersecting AD at point E.
6. Use a ruler to connect points B and E, creating the line segment BE.
7. Finally, label the points as A, B, and C.
To construct a perpendicular line from point C to line AB:
8. With C as the center and any radius greater than half of AB, draw two arcs intersecting line AB at points F and G.
9. With the same radius, draw arcs intersecting the arcs drawn in step 8 at points H and I.
10. Connect points G and I with a straight line.
11. The line CI is the perpendicular from point C to line AB, and it meets line AB at point P.
To extend line CP to create a point D such that BC = BD:
12. Use a compass to measure the length of BC from point C.
13. Without changing the compass width, place the compass point on point P and draw an arc away from line CP.
14. Keeping the same compass width, place the compass point on point C and draw another arc intersecting the first arc. Label this intersection point as D.
15. Connect points C and D with a straight line.
To measure |AC| and |AD|:
16. Use a ruler to measure the length of line segment AC, which is the distance between points A and C.
17. Use a ruler to measure the length of line segment AD, which is the distance between points A and D.
Using a pair of compasses and a ruler only, construct i.)∆ABC with|AB|=8cm, angle ABC=30°and angle CAB=45°.ii.)a perpendicular from the point C to meet the line AB at P. b.)i.) Extend line CP to the point D such that|BC|=|BD|.ii.) join A to D and B to D iii.) measure|AC|and|AD|
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