In the figure m and n are mid point of ab and ac if length of bc is 15cm length of mn
Answers
Answer:
PLZ REFER THE DIAGRAM IN THE ATTACHMENT BELOW!
Step-by-step explanation:
Here, In △ABC, M and N are the midpoints of sides AB and AC respectively. D and E are joined.
Given: AM = DB and AN = NC.
WE WILL CALCULATE THE VALUE OF MN BY MIDPOINT THEOREM
BECAUSE WE CAN'T CALCULATE IT BY SOMETHING ELSE :)
Construction: Extend line segment MN to F such that MN = NF.
In △ AMN and △ CFN,
AN = NC (given)
∠ANM = ∠CNF (vertically opposite angles)
MN = NF (construction)
hence
△AMN ≅ △ CFN (by SAS)
Therefore,
∠AMN = ∠CFN (by c.p.c.t.)
∠MAN = ∠FCN (by c.p.c.t.)
and AM = CF (by c.p.c.t.)
The angles ∠AMN and ∠CFE are alternate interior angles assuming AB and CF are two lines intersected by transversal DF.
Similarly, ∠DAE and ∠FCN are alternate interior angles assuming AB and CF are two lines intersected by transversal AC.
Therefore, AB ∥ CF
So, BD ∥ CF
and BM = CF (since AM = BM and it is proved above that AM = CF)
Thus, BMFC is a parallelogram.
By the properties of parallelogram, we have
MF ∥ BC
and MF = BC
ME ∥ BC
and MN = 1/2 BC (MN = NF by construction)
Hence proved.
MN = 1/2 BC
BC = 15 cm
MN = 1/2 *15
MN = 7.5 cm
HOPE IT HELPS !
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Answer:
7.5 cm is the correct answer.