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प्रश्न
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.
उत्तर
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.
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संबंधित प्रश्न
Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown
Construct a ABC in which BC = 6.5 cm, ABC = 60°, AB = 5 cm.
Using a ruler and compasses only:
1) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ABC = 120°
2) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
3) Measure ∠BCP.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
- What do you call the point O?
- What is the relation between the distances OA, OB and OC?
- Does the perpendicular bisector of BC pass through O?
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 a triangle ABC in which AB=S cm, BC=6 cm and CA=4.5 cm. Construct a circle passing through A, Band c.
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?
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.
In triangle ABC, ∠ABC = 90°, AB = 6 cm, BC = 7.2 cm and BD is perpendicular to side AC. Draw circumcircle of triangle BDC and then state the length of the radius of this circumcircle drawn.
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.
(i) Construct a triangle ABC, in which AB = 5.0 cm, BC = 3.5 cm and ∠ ABC = `67 1/2°`
( Use a pair of compasses and ruler only.)
(ii) Construct a circle to touch AB at B and it pass though C.
