D and E are points on the sides ab and ac of triangle abc such that ad 1.4cm bd 4.2cm ae 1.8cm ec 5.4cm show that parallel to bc
Answers
Answer:
Here, using the corollary of basic proportionality theorem which states that if a line passing through the two sides of the triangle cuts it proportionally, then the line is parallel to the third side. So,
(i)
AD
AB
=
8
12
=
2
3
AE
AC
=
12
18
=
2
3
∴
AD
AB
=
AE
AC
Thus, as DE cuts the sides AB and AC proportionally, so
DE∥BC.
∴ DE∥BC
(ii)
AD
AB
=
1.4
5.6
=4
AE
AC
=
1.8
7.2
=4
∴
AD
AB
=
AE
AC
Thus, as DE cuts the sides AB and AC proportionally, so
DE∥BC.
∴ DE∥BC
(iii)
BD
AD
=
4.5
10.8−4.5
=
4.5
6.3
=
5
7
EC
AE
=
4.8−2.8
2.8
=
2
2.8
=
5
7
∴
BD
AD
=
EC
AE
Thus, as DE cuts the sides AB and AC proportionally, so
DE∥BC.
∴ DE∥BC
(iv)
BD
AD
=
9.5
5.7
=
5
3
EC
AE
=
5.5
3.3
=
5
3
∴
BD
AD
=
EC
AE
Thus, as DE cuts the sides AB and AC proportionally, so
DE∥BC.