In triangle abc, ab= 6 cm and ac =3 CM .if m is the midpoint of ab and a straight line through and parallel to AC cuts B in N , what is the length of MN.
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Answer:
IN ΔAMN ΔABC
Since MN∣∣BC
∠AMN=∠ABC (Corresponding angles)
∠ANM=∠ACB (Corresponding angles)
∴ΔAMN∼ΔABC(By $$AA similarity criterion)
⇒
AB
AM
=
AC
AN
=
BC
MN
(CPST)
Since, M is mid-point of AB,
AM=
2
1
AB,or,
AB
AM
=
2
1
or,
AB
AM
=
AC
AN
=
2
1
AC
AN
=
2
1
5
AN
=
2
1
[∵AC=5cm]
AN=
2
5
cm=2.5cm
Also,
AB
AM
=
BC
MN
=
2
1
7
MN
=
2
1
[∵BC=7cm]
MN=
2
7
=3.5
Ans=AN=2.5cm and MN=3.5cm
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