Question

Draw a triangle ABC with AB = 6 cm, BC = 7 cm and CA = 8 cm. Using ruler and compass alone, draw (i) the bisector AD of ∠A and (ii) perpendicular AL from A on BC. Measure LAD.

Answer 1

Steps of construction:

1. Draw a line segment BC of length 7 cm.
2. With centre B, draw an arc of radius 6 cm.
3. With centre C, draw an arc of radius 8 cm intersecting the previously drawn arc at A.
4. Join AC and BC to get the required triangle.

Angle bisector steps:

1. From A, cut arcs of equal radius intersecting AB and AC at E and F, respectively.

2. From E and F, cut arcs of equal radius intersecting at point H.

3. Join AH and extend to produce the angle bisector of angle A, meeting line BC at D.

Perpendicular from Point A to line BC steps:

1. From A, cut arcs of equal radius intersecting BC at P and Q, respectively (Extend BC to draw these arcs).

2. From P and Q, cut arcs of equal radius intersecting at M.

3. Join AM cutting BC at L.

4. AL is the perpendicular to the line BC.

5. Angle LAD is 15^o.