Using a ruler and pair of compasses, Construct triangle ABC with AB=10cm, angle ABC=30 and angle BAC=45 .
To construct triangle ABC, follow these steps using a ruler and pair of compasses:
1. Draw a line segment AB of length 10cm using the ruler.
2. Place the compasses' point on point A and draw an arc that intersects line AB. Label this point of intersection as point C.
3. Without changing the compasses' width, place the point on point B and draw an arc that intersects line AB. Label this point of intersection as point D.
4. Using the ruler, draw a line segment CD, which will be one side of the triangle.
5. Place the point of the compasses on point C, adjust the width to a convenient distance, and draw an arc that intersects line CD. Label this point of intersection as point E.
6. With the compasses' width unchanged, place the point on point D, draw an arc intersecting line CD, and label this point of intersection as point F.
7. With the compasses' width unchanged, place the point on point E and draw an arc intersecting the arc drawn from point F. Label this point of intersection as point G.
8. Draw a line segment CG, which is another side of the triangle.
9. Finally, draw a line segment AG, which represents the third side of the triangle.
Triangle ABC has been constructed with AB = 10cm, angle ABC = 30°, and angle BAC = 45° using a ruler and pair of compasses.