Check whether AD is bisector of angle A of ∆ABC in each of the following
AB=4cm, AC=6cm, BD=1.6cm, CD=2.4cm
Answers
If a line through one vertex of a triangle divides the opposite side in the ratio of the other two sides, then the line bisects the angle at the vertex.
That is if
AC
AB
=
DC
BD
then ∠BAD=∠CAD
1)
AB=5cm
AC=10cm
BD=1.5cm
CD=3.5cm
AC
AB
=
10
5
=0.5 (1)
CD
BD
=
3.5
1.5
≈0.43 (2)
(1)
=(2)
Hence AD is not the bisector of ∠A of △ ABC
2)
AB=4cm
AC=6cm
BD=1.6cm
CD=2.4cm
AC
AB
=
6
4
≈0.67 (1)
CD
BD
=
2.4
1.6
≈0.67 (2)
(1)=(2)
Hence AD is the bisector of ∠A of △ ABC
3)
AB=8cm
AC=24cm
BD=6cm
BC=24=BD+DC=6+DC
CD=18cm
AC
AB
=
24
8
≈0.33 (1)
CD
BD
=
18
6
≈0.33 (2)
(1)=(2)
Hence AD is the bisector of ∠A of △ ABC
4)
AB=6cm
AC=8cm
BD=1.5cm
CD=2cm
AC
AB
=
8
6
=0.75 (1)
CD
BD
=
2
1.5
=0.75 (2)
(1)=(2)
Hence AD is the bisector of ∠A of △ ABC
5)
AB=5cm
AC=12cm
BD=2.5cm
BC=9=BD+DC=2.5+DC
CD=6.5cm
AC
AB
=
12
5
≈0.42 (1)
CD
BD
=
6.5
2.5
≈0.38 (2)
(1)
=(2)
Hence AD is not the bisector of ∠A of △ ABC