in a tringle ABC, AB =6cm and AC=3cm. If M is the mid point of AB and a staight line through M is parallel to AC cuts BC at N then what is the length of MN?
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Answer:
MN = 3.5cm
Step-by-step explanation:
In /\ AMN /\ ABC
since MN || BC
<AMN = < ABC ( correspnding angles)
<ANM = <ACB ( corresponding angles )
therefore /\ AMN ~ /\ ABC ( By $$AA similarly criterion)
=> AM = AN = MN ( CPST )
AB AC BC
Since M is rhe mid point of AB,
AM = 1 AB ,or ,AM = 1
2 AB 2
or AM = AN =1
AB AC 2
AN = 1
AC 2
AN = 1 [ °.° AC = 5cm]
5 2
AN = 5 cm = 2.5cm
also, AM = NM = 1
AB BC 2
MN = 1 [°.° BC = 7 cm ]
7 2
7 [ °.° BC = 7cm ]
MN = 2
MN = 7 = 3.5 cm
2
ans AN = 2.5cm and MN = 3.5 cm
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