8. In triangle ABC: M is mid-point of AB. Nis
mid-point of AC and D is any point in base
BC. Use Intercept Theorem to show that MN
bisects AD
Answers
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2
Answer:
In △AMN and △ABC
∠MAN=∠BAC .....(common)
AB
AM
=
AC
AN
=
2
1
∴△AMN is similar to △ABC
∴∠AMN=∠ABC⟶1
In △AMO and △ABD
⇒∠MAO=∠BAD ....(common)
⇒∠AMO=∠ABD .....(From equation 1)
⇒AM=2AB
Therefore, △AMO and △ABC are similar.
Thus
AB
AM
=
AD
AO
⇒
2AM
AM
=
AD
AO
⇒AD=2AO
⇒AO=AD
Therefore, MN bisects AD
Hence, proved.
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