Question

In a triangle ABC:
M is mid-point of AB
A straight line through M, parallel to BC cuts AC at N
BC = 16cm
Ac = 7cm
Find the lengths of AN & MN

Answer 1

Answer:

Step-by-step explanation:N 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