using a pair of compasses and ruler only construct triangle ABC, such that Ab=10cm <BAC=60 and <ABC = 90
To construct triangle ABC using a pair of compasses and a ruler, follow these steps:
1. Start by drawing a straight line segment using the ruler, and label the endpoints as points A and B. The length of AB should be 10 cm, as given.
2. Place the point of the compass on point B and adjust the compass width to approximately more than half the length of AB. This will be used to construct a perpendicular bisector.
3. Draw two arcs, one above and one below point B, intersecting the line AB. Label the points of intersection as C and D.
4. With the compass width still set as before, place the point of the compass on point C and draw an arc that intersects the first arc drawn (below point B). Let the point of intersection be denoted as E.
5. Using the ruler, draw a straight line connecting points C and E. This line is the perpendicular bisector of AB.
6. Place the point of the compass on point A and adjust the compass width to a suitable length.
7. Draw an arc that intersects the perpendicular bisector line at point F, which should be on the opposite side of AB as point C.
8. Lastly, draw a straight line connecting points B and F. This line segment BF represents the altitude from the vertex B to the base AC and should form a right angle (90 degrees) at point B.
Now, you have successfully constructed triangle ABC with the given specifications: AB = 10 cm, ∠BAC = 60 degrees, and ∠ABC = 90 degrees.