Ruler / compasses constructions exercises

1.

Given is a line l and a point P, not on l.
construct the reflexion of P in l. (call this point P').
Only use compasses.

2.

Given is a circle.
Construct the center.

3.

Construct an angle of 75 degrees.

4.

Construct an angle that is twice a given angle.

5.

Given are two circles and their centers.
Construct a line that is the tangent of both circles.

6.

Construct an equilateral triangle if only the length of the perimeter is given.

7.

Construct triangles ABC if given:

a. base AB, base angle LA and the sum AC + BC
b. base AB, base angle LA and the difference AC - BC
c. base angles LA and LB and the sum AC + BC
d. base AB and the distances from A and B to the opposite edges.

8.

Divide a linepiece in parts having ratio 2 : 3

9.

Construct a linepiece with length root(3) when a line with length 1 is given.

10.

Construct perpendicular triangle ABC (LC = 90 degrees) if given:
a. the distance of C to the opposite edge and also the length of median from C
b. hypothenusa AB and the sum AB + BC

11.

Only use compasses for this construction:
(use result of exercise 1.)

Given is a circle and it's center M and also a point P outside the circle and a point Q inside the circle.
Construct the intersection of line PQ and the circle.

12.

Construct a rhombus ABCD when given angle A ( < 90 degrees) and the sum AC + BD (diagonals).



Click [ here ] for the answers.