Question

Question 4
Construct a triangle whose sides are 3.6cm , 3.0cm and 4.8cm. bisects the smallest angle and measure each part.

Answer 1

To construct a triangle ABC in which AB = 3.6cm, AC = 3.0cm and BC = 4.8cm, use the following steps.

(i) Draw a line segment BC of length 4.8cm

(ii) From B, point A is at a distance of 3.6cm. So, having B as the centre, draw an arc of radius 3.6cm.

(iii) From C, point A is at a distance of 3cm. So, having C as the centre, draw an arc of radius 3cm which intersect the previous arc at A.

(iv) Join AB and AC, thus,$\Delta ABC$ is the required triangle.

Here, angle B is smallest, as AC is the smallest side (Angle opposite to the smallest side is smaller)

To bisect angle B, we use the following steps.

(i) Taking B as the centre, we draw arcs intersecting AB and BC at D and E, respectively.

(ii) Taking D and E as centres we draw arcs intersecting at P.

(iii) Joining BP, we obtain angle bisector of $\angle B$

(iv) Here, $\angle ABC={39}^{\circ }$

Thus,
$\angle ABP=\angle PBC=\frac{1}{2}\times {39}^{\circ }={19.5}^{\circ }$