Advertisements
Advertisements
Questions
Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.
Draw a regular hexagon of side 5 cm.
Solution
Steps of construction:
- Draw AF measuring 5 cm using a ruler.
- With A as the centre and radius equal to AF, draw an arc above AF.
- With F as the centre, and the same radius cut the previous arc at Z.
- With Z as the centre and same radius draw a circle passing through A and F.
- With A as the centre and same radius, draw an arc to cut the circle above AF at B.
- With B as the centre and same radius, draw ar arc to cut the circle at C.
- Repeat this process to get remaining vertices of the hexagon at D and E.
- Join consecutive arcs on the circle to form the hexagon.
- Draw the perpendicular bisectors of AF, FE and DE.
- Extend the bisectors of AF, FE and DE to meet CD, BC and AB at X, L and O respectively.
- Join AD, CF and EB.
- These are the 6 lines of symmetry of the regular hexagon.
APPEARS IN
RELATED QUESTIONS
Using ruler and compasses only, draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the circle.
Contruct a ΔABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incricle.
Using ruler and compasses only, construct Δ ABC in which BC=7.5 cm, ∠ ABC = 60° and AC - AB= 1.5 cm. Inscribe a circle in the Δ ABC and measure its radius.
Draw a circle of radius 2. 5 cm and circumscribe a square about it.
Draw a line segment OA , 5 cm long. AT O , using ruler and compasses only, construct OB such that , ∠ AOB = 37.5° construct a circle to touch OA at A and to touch OB at B.
Draw line segments OA = 4.5 cm, OB = 3.2 cm such that ∠ AOB = 45°. Construct a circle touching OA at A and passing through B.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
What is the relation between the distances OA, OB and OC?
Using ruler and compass only, construct a triangle ABC such that AB = 5 cm, ABC = 75°, and the radius of the circumcircle of triangle ABC is 3.5 cm. On the same diagram, construct a circle, touching AB at its middle point and also touching the side AC.
Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
Construct a ΔABC with base BC = 3.5 cm, vertical angle ∠ BAC = 45°, and median through the vertex A is 3.5 cm. Write also the steps of construction.
