Using a ruler and a pair of compasses only, construct :(i)a triangle ABC with BC=9cm,AC=8cm, and AB=6cm;(ii) the perpendicular bisector of line BC;(iii) the bisector of angle ACB.
(i) To construct triangle ABC with BC = 9cm, AC = 8cm, and AB = 6cm, follow these steps:
Step 1: Draw a line segment AB = 6cm.
Step 2: Place the compass at point A and draw an arc with a radius of 8cm to intersect the line segment AB. Label the point of intersection as C.
Step 3: Without changing the compass width, place the compass at point B and draw an arc.
Step 4: Keeping the same width, place the compass at point C and draw an arc to intersect the previously drawn arc. Label the point of intersection as A.
Step 5: Connect points A, B, and C to form triangle ABC.