# Constructions

## Exercise

**Use ruler and compass only for the following questions**

- Construct an equilateral triangle having altitude = 4.3 cm.
- Construct a triangle ABC with BC = 4.8 cm, CA = 5.2 cm and median AM = 5.4 cm.
- Construct an isosceles triangle PQR with base PQ = 5.7 cm and altitude RM to the base PQ = 4.3 cm.
- Construct an isosceles triangle ABC given that base BC = 6 cm
and vertical A = 120°.

[**Hint.**Each base angle = 30°] - Construct a right angled triangle ABC right angled at B and CA = 2 BC = 5.8 cm.
- Construct an isosceles right angled triangle with hypotenuse 5.7 cm.
- Draw a quadrilateral ABCD with AB = 6 cm, BC = 4 cm, CD = 4 cm and B = C = 90°.
- Construct a quadrilateral ABCD in which AB = 5 cm, BC = 2.5 cm, CD = 6 cm, BAD = 90° and diagonal AC = 5.5 cm.
- Construct a parallelogram ABCD with diagonal AC = 4 cm, diagonal BD = 6 cm and containing an angle of 75°.
- Construct a rectangle PQRS such that PQ = 3.5 cm and RPS = 75°.
- Construct a rectangle whose one diagonal is 6.8 cm and an angle between two diagonals is 105°.
- Construct a rhombus whose diagonals are 7 cm and 5.3 cm.
- Construct a square whose one diagonal is 5.8 cm.
- Draw a line segment AB = 4.9 cm. Construct a circle with AB as diameter.
- Draw a line segment PQ = 4.1 cm. Construct a circle of radius 2.6 cm and passing through the points P and Q.
- Construct a triangle ABC having AB = 2.3 cm, BC = 5.4 cm and B = 120°. Also construct the circumcircle of this triangle.
- Construct a triangle ABC given that BC = 4.7 cm, C = 60° and median BM = 4 cm. Also construct the incircle of this triangle.