Question

question #18
trapezoid abcd is congruent to trapezoid jklm shown below.
which of these proportions is true?
a \\(\frac{ab}{kl} = \frac{bc}{lm}\\)
b \\(\frac{ad}{dc} = \frac{kj}{lm}\\)
c \\(\frac{ad}{jm} = \frac{bc}{kl}\\)
d \\(\frac{dc}{ml} = \frac{ab}{kl}\\)

Explanation:

Step1: Identify congruent side pairs

Congruent trapezoids have matching sides: $AB=KL$, $BC=LM$, $CD=MJ$, $DA=JK$

Step2: Test each proportion

For Option A:

Substitute congruent sides: $\frac{AB}{KL}=\frac{KL}{KL}=1$, $\frac{BC}{LM}=\frac{LM}{LM}=1$. So $\frac{AB}{KL}=\frac{BC}{LM}=1$

For Option B:

$\frac{AD}{BC}=\frac{JK}{LM}$, which is not equal to $\frac{KJ}{LM}$ (since $JK=KJ$ but $\frac{JK}{LM}
eq\frac{KJ}{LM}$ only if $JK=LM$, which is not given)

For Option C:

$\frac{AD}{JM}=\frac{JK}{CD}$, $\frac{BC}{KL}=\frac{LM}{AB}$. These are not equal as $JK
eq LM$ and $CD
eq AB$

For Option D:

$\frac{DC}{ML}=\frac{MJ}{LM}$, $\frac{AB}{KL}=\frac{KL}{KL}=1$. These are not equal as $MJ
eq LM$

Answer:

A. $\frac{AB}{KL} = \frac{BC}{LM}$