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.
Please answer fast.
Answers
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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