In triangle MNS, A and B are points on the sides MN, NS respectively.Then AB is …………………. to NS :a)Not Perpendicularb)Parallelc)Perpendiculard)Not ParallelCorrect answer is option 'B'. Can you explain this answer?

Question

In triangle MNS, A and B are points on the sides MN, NS respectively.Then AB is &hellip;&hellip;&hellip;&hellip;&hellip;&hellip;&hellip;. to NS :a)Not Perpendicularb)Parallelc)Perpendiculard)Not ParallelCorrect answer is option 'B'. Can you explain this answer?

Answer

If a line divides any two sides of a triangle in the same ratio then the line is parallel to the third side.(by convers of thales theorem)

Answer

Correct answer is option 'B'

Answer

In ∆MNS we have,

→ AN = 1/2(MN)
→ AN = (1/2)(MA + AN)
→ AN = (1/2)MA + (1/2)AN
→ AN - (1/2)AN = (1/2)MA
→ AN[1 - (1/2)] = (1/2)MA
→ (1/2)AN = (1/2)MA
→ AN = MA
so, A is mid point of MN .

similarly,
→ BS = (1/2)(MS)

so, B is mid point of MS .

since AB is a line segment joining the mid points of two sides of ∆MNS .

therefore, → AB || NS { According to Mid point theorem the line segment joining the mid points of two sides of a triangle is parallel to the third side . }

Answer

In ∆MNS we have,

→ AN = 1/2(MN)
→ AN = (1/2)(MA + AN)
→ AN = (1/2)MA + (1/2)AN
→ AN - (1/2)AN = (1/2)MA
→ AN[1 - (1/2)] = (1/2)MA
→ (1/2)AN = (1/2)MA
→ AN = MA
so, A is mid point of MN .

similarly,
→ BS = (1/2)(MS)

so, B is mid point of MS .

since AB is a line segment joining the mid points of two sides of ∆MNS .

therefore, → AB || NS { According to Mid point theorem the line segment joining the mid points of two sides of a triangle is parallel to the third side . }

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