basic geometrical constructions

SMPK PENABUR GS

BASIC GEOMETRICAL CONSTRUCTIONS

Constructing a 900 Angle

Step 1Draw a line with the measure is 5 cm

5 cm


Step 2Draw point A at the line

A


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

P QA


Step 4Place the point of the compass at P and draw an arc that passes through Q

P QA


Step 5Place 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.

P QA

R


Step 6By using ruler, joint A to R, so angle RAQ is 900

P QA

R

900


Step 1Draw the arm PQ.

P Q


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

P Q


Step 3Place 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.

P Q

R


Step 4 Join P to R. The angle QPR is 60o

P Q

R

600


We know that, x 600 = 300

So, to construct an angle of 30º, first construct a 60º angle and then bisect it.


Step 1 Construct 600 angle

P Q

R

600


Step 2 With the point of the compass at P , draw an arc intersecting arm PQ at M and intersecting arm PR at N.

P Q

R

600

M

N


Step 3 At point M and N draw an arc with same radius then intersect at point T

P Q

R

600

M

N

T


Step 4 Join P to T. Then angle TPQ is 300

P Q

R

600

M

N

T

300

Your TurnConstruct the angle below by using compass and ruler :a. 450

b. 22,5c. 150

d. 67,50

e. 52,50

Constructing a 450 angle

We know that,

x 900 = 450

So, to construct an angle of 45º, first construct a 90º angle and then bisect it.


Step 1Construct 900 angle

P Q

R


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

P Q

R

A

B


Step 3Put your Compass at the point A and B then draw an arc with the same radius so intersect each other at the point C

P Q

R

A

B

C


Step 4Joint P to C, so angle CPQ is 450

P Q

R

A

B

C

450

Technology