Question

6. In AABC, M and N are mid-points of AB
and AC, and NP || AB.
(i) Prove that BMNP is a parallelogram.
(ii) If AB = 11 cm, BC = 12 cm, find the
perimeter of BMNP.
N
M
B.
P
С​

Answer 1

Answer:

SinceM,N,andParethemid−pointsofAB,ACandBCrespectively.

HenceMN=  

2

1

​  

BC

⟹BC=2MN

⟹BC=2×3=6cm

SimilarlyAC=2MP=2×2.5=5cm

andAB=2NP=2×3.5=7cm

Step-by-step explanation:

Answer 2

Given : In AABC, M and N are mid-points of AB and AC, and NP || AB.

To Find :  

(i) Prove that BMNP is a parallelogram.

(ii) If AB= 11 cm, BC = 12 cm, find the perimeter of BMNP.

Solution:

line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to third side

M and N are mid-points of AB and AC,

=> MN = BC/2  and MN || BC

MN || BC =>  MN || BP  as P is a point on BC

NP || AB  given

Hence BMNP is a parallelogram.

Perimeter = BMNP

= BM + MN + NP + BP

= 2 ( BM + MN)

= 2( AB/2  + BC/2)

= AB + BC

= 11 + 12

= 23 cm

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