Using a ruler and a pair of compass only construct
I.Triangle ABC such that
AB=12cm,AC=8cm and angle BAC=30°.
To construct triangle ABC with given dimensions and angle using just a ruler and a pair of compasses, follow these steps:
1. Start by drawing a straight line segment AB of 12cm length using the ruler.
2. Place the pointed end of the compass at point A and draw an arc with a radius of 8cm to intersect line segment AB. Mark this point as C.
3. Without changing the compass radius, place the pointed end of the compass at point C and draw another arc to intersect the first arc you drew. Label this point of intersection as D.
4. Now, place the pointed end of the compass at point D and draw an arc with a radius that intersects line segment AB. Label this point as E.
5. Place the pointed end of the compass at point E and draw an arc with a radius that intersects the second arc you drew in step 3. This will create another point of intersection, label it as F.
6. Using the ruler, draw a line segment from point F to point A.
7. Finally, connect point B to points C and F to complete the triangle ABC.
You have now constructed triangle ABC with side lengths AB=12cm, AC=8cm, and angle BAC=30° only using a ruler and a pair of compasses.