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BASIC GEOMETRICAL
 CONSTRUCTIONS
    SMPK PENABUR GS
Constructing a                   900   Angle
Step 1
Draw a line with the measure is 5 cm




                        5 cm
Constructing a                900   Angle
Step 2
Draw point A at the line




                           A
Constructing a                  900     Angle
Step 3
Place the point of the compass at A and draw an arc
that passes through the line at point P and Q




                P        A         Q
Constructing a                   900    Angle
Step 4
Place the point of the compass at P and draw an arc that
passes through Q




                 P       A         Q
Constructing a                  900     Angle
Step 5
Place the point of the compass at Q and draw an arc
that passes through P that cuts the arc drawn in Step 4
at R.
                         R




                P        A         Q
Constructing a                    900     Angle
Step 6
By using ruler, joint A to R, so angle RAQ is 900


                          R




                           900
                 P        A         Q
Constructing a     600   Angle
Step 1
Draw the arm PQ.




           P         Q
Constructing a                   600      Angle
Step 2
Place the point of the compass at P and draw an arc that
passes through Q.




             P                         Q
Constructing a                   600      Angle
Step 3
Place the point of the compass at Q and draw an arc
that passes through P. Let this arc cut the arc drawn in
Step 2 at R.

                          R




             P                         Q
Constructing a                     600   Angle
Step 4
Join P to R. The angle QPR is 60o



                          R




                  600
             P                        Q
Constructing a   30 0   Angle
Constructing a             30 0   Angle
Step 1
Construct 600 angle


                       R




                 600
            P                 Q
Constructing a                  30 0     Angle
Step 2
With the point of the compass at P , draw an arc
intersecting arm PQ at M and intersecting arm PR at N.

                           R




                N

                 600
            P                        Q
                       M
Constructing a                  30 0     Angle
Step 3
At point M and N draw an arc with same radius then
intersect at point T

                           R
                                                     T




                N

                 600
            P                        Q
                       M
Constructing a                   30 0    Angle
Step 4
Join P to T. Then angle TPQ is 300


                            R
                                            T




                N

                 600       300
            P                        Q
                       M
Your Turn
Construct the angle below by using compass and ruler :
a. 450
b. 22,5
c. 150
d. 67,50
e. 52,50
Constructing a   450   angle
Constructing a          450   angle
Step 1
Construct 900 angle
                      R




                      P    Q
Constructing a                   450     angle
Step 2
Put your Compass at the point P, and draw an arc
intersect PQ and PR at A and B.



                       R




                   B


                       P     A        Q
Constructing a                      450     angle
Step 3
Put your Compass at the point A and B then draw an arc
with the same radius so intersect each other at the point C


                                                    C
                         R




                     B


                         P      A        Q
Constructing a                     450   angle
Step 4
Joint P to C, so angle CPQ is 450



                                            C
                        R




                    B
                              450

                        P     A      Q

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Basic geometrical constructions

  • 2. Constructing a 900 Angle Step 1 Draw a line with the measure is 5 cm 5 cm
  • 3. Constructing a 900 Angle Step 2 Draw point A at the line A
  • 4. Constructing a 900 Angle Step 3 Place the point of the compass at A and draw an arc that passes through the line at point P and Q P A Q
  • 5. Constructing a 900 Angle Step 4 Place the point of the compass at P and draw an arc that passes through Q P A Q
  • 6. Constructing a 900 Angle Step 5 Place the point of the compass at Q and draw an arc that passes through P that cuts the arc drawn in Step 4 at R. R P A Q
  • 7. Constructing a 900 Angle Step 6 By using ruler, joint A to R, so angle RAQ is 900 R 900 P A Q
  • 8. Constructing a 600 Angle Step 1 Draw the arm PQ. P Q
  • 9. Constructing a 600 Angle Step 2 Place the point of the compass at P and draw an arc that passes through Q. P Q
  • 10. Constructing a 600 Angle Step 3 Place the point of the compass at Q and draw an arc that passes through P. Let this arc cut the arc drawn in Step 2 at R. R P Q
  • 11. Constructing a 600 Angle Step 4 Join P to R. The angle QPR is 60o R 600 P Q
  • 12. Constructing a 30 0 Angle
  • 13. Constructing a 30 0 Angle Step 1 Construct 600 angle R 600 P Q
  • 14. Constructing a 30 0 Angle Step 2 With the point of the compass at P , draw an arc intersecting arm PQ at M and intersecting arm PR at N. R N 600 P Q M
  • 15. Constructing a 30 0 Angle Step 3 At point M and N draw an arc with same radius then intersect at point T R T N 600 P Q M
  • 16. Constructing a 30 0 Angle Step 4 Join P to T. Then angle TPQ is 300 R T N 600 300 P Q M
  • 17. Your Turn Construct the angle below by using compass and ruler : a. 450 b. 22,5 c. 150 d. 67,50 e. 52,50
  • 18. Constructing a 450 angle
  • 19. Constructing a 450 angle Step 1 Construct 900 angle R P Q
  • 20. Constructing a 450 angle Step 2 Put your Compass at the point P, and draw an arc intersect PQ and PR at A and B. R B P A Q
  • 21. Constructing a 450 angle Step 3 Put your Compass at the point A and B then draw an arc with the same radius so intersect each other at the point C C R B P A Q
  • 22. Constructing a 450 angle Step 4 Joint P to C, so angle CPQ is 450 C R B 450 P A Q