Answer:
AB = M₂M₁
Step-by-step explanation:
See attached diagram of trapezium ABCD.
(i) Triangle ABN and triangle CND are similar, so we can write a proportion:
AN / NC = AB / CD
AN / NC = a / 3a
AN / NC = 1 / 3
(ii) M₂ is the midpoint of AC, so:
2 AM₂ = AC
2 (AN + NM₂) = AN + NC
2 AN + 2NM₂ = AN + NC
AN + 2NM₂ = NC
1 + 2NM₂ / AN = NC / AN
1 + 2NM₂ / AN = 3
2NM₂ / AN = 2
NM₂ / AN = 1
Triangle ABN and triangle M₂M₁N are similar, so:
AB / M₂M₁ = AN / NM₂
AB / M₂M₁ = 1
AB = M₂M₁
