Question

5 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 ZA and (i) perpendicular AL from A on BC.
Measure LAD.​

Answer 1

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$\Large\bold{\underline{\pink{Construction:}}}$

$\small\bold\orange{Step:1}$

Draw a line segment BC of length 7 cm.

$\small\bold\orange{Step:2}$

With center B, draw an arc of radius 6 cm.

$\small\bold\orange{Step:3}$

With center C, draw an arc of radius 8 cm intersecting the previously drawn arc at A.

$\small\bold\orange{Step:4}$

Join AC and BC to get the required triangle.

$\small\bold\orange{Step:5}$

Angle bisector from A, cut arcs of equal radius intersecting AB and AC at E and F, respectively.

$\small\bold\orange{Step:6}$

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

$\small\bold\orange{Step:7}$

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

$\small\bold\orange{Step:8}$

Perpendicular from Point A to line BC steps. From A, cut arcs of equal radius intersecting BC at P and Q, respectively (Extend BC to draw these arcs).

$\small\bold\orange{Step:9}$

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

$\small\bold\orange{Step:10}$

Join AM cutting BC at L.

$\small\bold\orange{Step:11}$

AL is the perpendicular to the line BC.

$\small\bold\orange{Step:12}$

Angle LAD is 15°

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