Question

Fig. 1.18
Activity:
Draw a A ABC.
Bisect B and name the point
of intersection of AC and the
angle bisector as D.
Measure the sides.
Cm
cm
AB =
BC =
B
AD =
DC =
AB AD
Find ratios and
Fig. 1.19
BC DC
You will find that both the ratios are almost equal.
Bisect remaining angles of the triangle and find the ratios as above. You
can verify that the ratios are equal.
please see the image you will understand​

Answer 1

Given :  ΔABC

To Find : Verify that Ratio of sides containing angles and ratio in which angle bisector bisect opposite side is same

Solution:

Step 1 : Draw a line segment  BC = 8 cm

Step 2 : Using compass width = 4 cm draw an arc from B

Step 3 : Using compass width = 5 cm draw an arc from C Such that it intersects arc drawn in previous step at A

Step 4 : Join AB and AC

Step 5 : Using suitable compass width taking B as center draw an arc intersecting AB at M and BC at N

Step 6 : Using Suitable compass width  and taking M and N as center draw intersecting arcs at P

Step 7 Draw  a line  passing through BP and intersecting AC at D

Measure AD & CD

AB = 4 cm   BC = 8    AB/BC =  4/8 = 0.5

AD = 1.67 cm  CD = 3.33 cm  AD/AC  = 1.67/3.33 = 0.5

Similarly draw angle bisector of A  as  AE  

AB/AC = 4/5 = 0.8

BE/CE =  3.56/4.44 = 0.8

Similarly draw  angle bisector of  C  as  CF

BC/AC =8/5 = 1.6

BF/AF =  2.46/1.54 = 1.6

Verified that Ratio of sides containing angles and ratio in which angle bisector bisect opposite side is same

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