Question

state and prove p.p.t for the figure (geometry)...​

Answer 1

Step-by-step explanation:

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Answer 2

Given :- state and prove BPT for the figure ? (MN || YZ.)

To Prove :-

• BPT theorem :- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio .
• XM/MY = XN/NZ .

Consturction :-

• Join MZ ane NY .
• Draw MB ⟂ XZ and NA ⟂ XY .

Solution :-

we know that,

• Area of ∆ = (1/2) * Base * Perpendicular height .

so,

→ Area (∆XMN) / Area (∆MYN) = {(1/2) * XM * AN} / {(1/2) * MY * AN} = XM/MY ------- Eqn.(1)

and,

→ Area (∆XMN) / Area (∆NZM) = {(1/2) * XN * BM} / {(1/2) * NZ * BM} = XN/NZ ------- Eqn.(2)

now, as we can see that,

• ∆MYN and ∆NZM are on the same base MN and between same parallel lines MN and YZ .

Therefore, we can conclude that,

→ Area (∆MYN) = Area (∆NZM) --------- Eqn.(3)

hence, from Eqn.(1), Eqn.(2) and Eqn.(3) we get,

→ XM/MY = XN/NZ (Proved.)

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