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

Constructing a 900 Angle

Step 2Draw point A at the line

A

Constructing a 900 Angle

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

Constructing a 900 Angle

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

P QA

Constructing a 900 Angle

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

Constructing a 900 Angle

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

P QA

R

900

Constructing a 600 Angle

Step 1Draw 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 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

Constructing a 600 Angle

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

P Q

R

600

Constructing a 300 Angle

We know that, x 600 = 300

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

Constructing a 300 Angle

Step 1  Construct 600 angle

P Q

R

600

Constructing a 300 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.

P Q

R

600

M

N

Constructing a 300 Angle

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

Constructing a 300 Angle

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.

Constructing a 450 angle

Step 1Construct 900 angle

P Q

R

Constructing a 450 angle

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

Constructing a 450 angle

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

Constructing a 450 angle

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

P Q

R

A

B

C

450