Question

l, m, n are parallel lines. If p intersects them at A, B, C and q at D,E, F then:

• A. AB = DE and BC = EF always
• B. at least one of the pairs AB, DE and BC, EF are necessarily equal.
• C. at least one of the pairs AB, BC and DE, EF are necessarily equal.
• D. $\frac{AB}{BC}=\frac{DE}{EF}$

Answer 1

Answer: (D)

$\frac{AB}{BC}=\frac{DE}{EF}$

$ADFC$ forms a trapezium

$AD\parallel CF$ .............. (Since, bases of trapezium are parallel)

$AC$ congruent to $DF$ i.e. $AC=DF$ ........ (Since, opposite sides of a trapezium are congruent)

$\because$ $l,m,n$ are parallel

$\therefore$ The middle line $m$ divides $AC$ and $DF$ in equal ratio.

$\therefore$ $\frac{AB}{BC}=\frac{DE}{EF}$